Search results for: Radial Basis Functions

Authors: Chahid K. Ghaddar

Abstract:

The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

Abstract:

In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

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Authors: Yongzheng Li, Hongfang Ma, Qiwen Sun, Haitao Zhang, Weiyong Ying

Abstract:

Radial profiles of particle velocities were investigated in a 6.1 m tall methanol-to-olefins cold model experimental device using a TSI laser Doppler velocimeter. The measurement of axial levels was conducted in the full developed region. The effect of axial level on flow development was not obvious under the same operating condition. Superficial gas velocity and solid circulating rate had significant influence on particle velocity in the center region of the riser. Besides, comparisons between upward, downward and average particle velocity were conducted. The average particle velocity was close to upward velocity and higher than downward velocity in radial locations except the wall region of riser.

Keywords: circulating fluidized bed, laser doppler velocimeter, particle velocity, radial profile

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Authors: Ge Zheng, Jun Peng

Abstract:

Unbalanced power output from individual cells of Proton Exchange Membrane Fuel Cell (PEMFC) has direct effects on PEMFC stack performance, in particular under transient operation. In the paper, a multi-layer ANN (Artificial Neural Network) model Radial Basis Functions (RBF) has been developed for predicting cells' output profiles by applying gas supply parameters, cooling conditions, temperature measurement of individual cells, etc. The feed-forward ANN model was validated with experimental data. Influence of relevant parameters of RBF on the network accuracy was investigated. After adequate model training, the modelling results show good correspondence between actual measurements and reconstructed output profiles. Finally, after the model was used to optimize the stack output performance under steady-state and transient operating conditions, it suggested that the developed ANN control model can help PEMFC stack to have obvious improvement on power output under fast acceleration process.

Keywords: proton exchange membrane fuel cell, PEMFC, artificial neural network, ANN, cell output profile, transient

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Authors: Ramya Rathan, Miral N. F. Salama

Abstract:

The variations in the arteries have been drawing attention of anatomists for a long time because of their clinical significance. The brachial artery is the principal artery of the arm which is the continuation of the axillary artery from the lower border of the Teres Major. It terminates into the radial and ulnar arteries below the elbow joint at the neck radius. The present study aims at exploring the clinical significance of the high termination of the brachial artery. During the routine cadaveric dissection of the arm, for the undergraduate students of medicine at our university, we observed a high bifurcation of the radial and the ulnar artery at the midshaft of the humerus. The median nerve was seen passing between these two junctions. Further, the course and the relations of this artery were studied. The accurate knowledge regarding these kinds of variation in the blood vessels is mandatory for planning of designing. General physicians, surgeons and radiologists should keep in mind the variations in the branching pattern of the arteries in their daily medical, diagnostic and therapeutic procedures to avoid complications in diagnostic and surgical procedures.

Keywords: brachial artery, high termination, radial artery, ulnar artery

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Authors: F. A. Rodríguez-Prada, W Gutierrez, I. D. Mikhailov

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We study the spectral properties of one-electron non-uniform crater-shaped quantum dot whose thickness is increased linearly with different slopes in different radial directions between the central hole and the outer border and which is deposited over thin wetting layer in the presence of the external vertically directed magnetic field. We show that in the adiabatic limit, when the crater thickness is much smaller than its lateral dimension, the one-particle wave functions of the electron confined in such structure in the zero magnetic field case can be found exactly in an analytical form and they can be used subsequently as the base functions in framework of the exact diagonalization method to study the effect of the wetting layer and an external magnetic field applied along of the grown axis on energy levels of one-electron non-uniform quantum dot. It is shown that both the structural non-uniformity and the increase of the thickness of the wetting layer provide a quenching of the Aharonov-Bohm oscillations of the lower energy levels.

Keywords: electronic properties, quantum rings, volcano shaped, wetting layer

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Authors: Luiz F. J. Maia

Abstract:

This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

Abstract:

In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínez

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sᵩ is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Mehdi Rashidi-Kouchi, Asghar Rahimi

Abstract:

Sun introduced a generalization of frames and showed that this includes more other cases of generalizations of frame concept and proved that many basic properties can be derived within this more general context. Another generalization of frames is frames in Hilbert C*-module. It has been proved that every g-frame in Hilbert space H respect to Hilbert space K is a frame for B(H;K) as Hilbert C*-module. We show that every g-Riesz basis for Hilbert space H respect to K by add a condition is a Riesz basis for Hilbert B(K)-module B(H;K). Also, we investigate similar result for g-orthonormal and orthogonal bases.

Keywords: frame, g-frame, Riesz basis, g-Riesz basis, Hilbert C*-module

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Authors: Sumit Banerjee, Chandan Kumar Chanda

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The paper presents allocation of active power losses and energy losses to consumers connected to radial distribution networks in a deregulated environment for loads of composite types. A detailed comparison among four algorithms, namely quadratic loss allocation, proportional loss allocation, pro rata loss allocation and exact loss allocation methods are presented. Quadratic and proportional loss allocations are based on identifying the active and reactive components of current in each branch and the losses are allocated to each consumer, pro rata loss allocation method is based on the load demand of each consumer and exact loss allocation method is based on the actual contribution of active power loss by each consumer. The effectiveness of the proposed comparison among four algorithms for composite load is demonstrated through an example.

Keywords: composite type, deregulation, loss allocation, radial distribution networks

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Authors: Valentina Futoryanova, Hugh Hunt

Abstract:

One of the common failure modes of the diesel engine turbochargers is high cycle fatigue of the turbine wheel blades. Mistuning of the blades due to the casting process is believed to contribute to the failure mode. Laser vibrometer is used to characterize mistuning for a population of turbine wheels through the analysis of the blade response to piezo speaker induced noise. The turbine wheel design under investigation is radial and is typically used in 6-12 L diesel engine applications. Amplitudes and resonance frequencies are reviewed and summarized. The study also includes test results for a paddle wheel that represents a perfectly tuned system and acts as a reference. Mass spring model is developed for the paddle wheel and the model suitability is tested against the actual data. Randomization is applied to the stiffness matrix to model the mistuning effect in the turbine wheels. Experimental data is shown to have good agreement with the model.

Keywords: vibration, radial turbines, mistuning, turbine blades, modal analysis, periodic structures, finite element

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Authors: Tobias Beyer, Christoph Friedrich

Abstract:

Modern simulation methodology using finite element models is nowadays a recognized tool for product design/optimization. Likewise, manufacturing process design is increasingly becoming the focus of simulation methodology in order to enable sustainable results based on reduced real-life tests here as well. In this article, two process simulations -radial riveting and roller burnishing- used for mechanical joining of components are explained. In the first step, the required boundary conditions are developed and implemented in the respective simulation models. This is followed by process space validation. With the help of the validated models, the interdependencies of the input parameters are investigated and evaluated by means of sensitivity analyses. Limit case investigations are carried out and evaluated with the aid of the process simulations. Likewise, a comparison of the two joining methods to each other becomes possible.

Keywords: FEM, model-based process development, process simulation, radial riveting, roller burnishing, sensitivity analysis

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Authors: Shahin A. Abdel-Naby, James P. Colgan, Michael S. Pindzola

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A time-dependent close-coupling method is developed to calculate a total, double and triple autoionization rates for hollow atomic ions of four-electron systems. This work was motivated by recent observations of the four-electron Auger process in near K-edge photoionization of C+ ions. The time-dependent close-coupled equations are solved using lattice techniques to obtain a discrete representation of radial wave functions and all operators on a four-dimensional grid with uniform spacing. Initial excited states are obtained by relaxation of the Schrodinger equation in imaginary time using a Schmidt orthogonalization method involving interior subshells. The radial wave function grids are partitioned over the cores on a massively parallel computer, which is essential due to the large memory requirements needed to store the coupled-wave functions and the long run times needed to reach the convergence of the ionization process. Total, double, and triple autoionization rates are obtained by the propagation of the time-dependent close-coupled equations in real-time using integration over bound and continuum single-particle states. These states are generated by matrix diagonalization of one-electron Hamiltonians. The total autoionization rates for each L excited state is found to be slightly above the single autoionization rate for the excited configuration using configuration-average distorted-wave theory. As expected, we find the double and triple autoionization rates to be much smaller than the total autoionization rates. Future work can be extended to study electron-impact triple ionization of atoms or ions. The work was supported in part by grants from the American University of Sharjah and the US Department of Energy. Computational work was carried out at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California, USA.

Keywords: hollow atoms, autoionization, auger rates, time-dependent close-coupling method

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Authors: S. alireza Mirghasemi, Shervin Rashidinia, Mohammadsaleh Sadeghi, Mohsen Talebizadeh, Narges Rahimi Gabaran, S. Shahin Eftekhari, Sara Shahmoradi

Abstract:

Purpose: There are various pin-in-plaster methods for treating distal radius fractures. This study is meant to introduce a modified technique of pin-in-plaster. Materials and methods: Fifty-four patients with distal radius fractures were followed up for one year. Patients were excluded if they had type B fractures according to AO classification, multiple injuries or pathological fractures, and were treated more than 7 days after injury. Range of motion and functional results were evaluated. Radiographic parameters including radial inclination, tilt, and height, were measured preoperatively and postoperatively. Results: The average radial tilt was 10.6° and radial height was 10.2 mm at the sixth month postoperatively. Three cases of pin tract infection were recorded, who were treated totally with oral antibiotics. There was no case of pin loosening. Of total 73 patients underwent surgery, three cases of radial nerve irritation were recorded at the time of cast removal. All of them resolved at the 6th month follow up. No median nerve compression and carpal tunnel syndrome have found. We also had no case of tendon injury. Conclusion: Our modified technique is effective to restore anatomic congruity and maintain reduction.

Keywords: distal radius fracture, percutaneous pinning, pin-in-plaster, modified method of pin-in-plaster, operative treatment

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

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The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

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Authors: Erkingul Soltanaeva, Omyrkhan Abdimanuly, Alua Temirbolat

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In this article, the public and social functions of literature and art in the Republic of Kazakhstan were analyzed on the basis of formal and informal literary organizations. The external and internal, subjective and objective factors which influenced the modern literary process were determined. The literary forces, their consolidation, types of organization in the art of word were examined. The periods of the literary process as planning, organization, promotion, and evaluation and their leading forces and approaches were analyzed. The right point of view to the language and mentality of the society force will influence to the literary process. The Ministry of Culture, the Writers' Union of RK and various non-governmental organizations are having different events for the promotion of literary process and to glorify literary personalities in the entire territory of Kazakhstan. According to the cultural plan of different state administration, there was a big program in order to publish their literary encyclopedia, to glorify and distribute books of own poets and writers of their region to the country. All of these official measures will increase the reader's interest in the book and will also bring up people to the patriotic education and improve the status of the native language. The professional literary publications such as the newspaper ‘Kazakh literature’, magazine ‘Zhuldyz’, and journal ‘Zhalyn’ materials which were published in the periods 2013-2015 on the basis of statistical analysis of the Kazakh literature topical to the issues and the field of themes are identified and their level of connection with the public situations are defined. The creative freedom, relations between society and the individual, the state of the literature, the problems of advantages and disadvantages were taken into consideration in the same articles. The level of functions was determined through the public role of literature, social feature, personal peculiarities. Now the stages as the literature management planning, organization, motivation, as well as the evaluation are forming and developing in Kazakhstan. But we still need the development of literature management to satisfy the actual requirements of the today’s agenda.

Keywords: literature management, material, literary process, social functions

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Authors: R. Ghasemi, M. R. Rahimi Khoygani

Abstract:

This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: H. Al-Qassem, L. Cheng, Y. Pan

Abstract:

In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness

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Authors: Hau-Wei Lee, Yu-Chi Liu, Chien-Hung Liu

Abstract:

A mathematical model is presented for a system that measures rotational errors in a shaft using a ball lens. The geometric optical characteristics of the ball lens mounted on the shaft allows the measurement of rotation axis errors in both the radial and axial directions. The equipment used includes two quadrant detectors (QD), two laser diodes and a ball lens that is mounted on the rotating shaft to be evaluated. Rotational errors in the shaft cause changes in the optical geometry of the ball lens. The resulting deflection of the laser beams is detected by the QDs and their output signals are used to determine rotational errors. The radial and the axial rotational errors can be calculated as explained by the mathematical model. Results from system calibration show that the measurement error is within ±1 m and resolution is about 20 nm. Using a direct drive motor (DD motor) as an example, experimental results show a rotational error of less than 20 m. The most important features of this system are that it does not require the use of expensive optical components, it is small, very easy to set up, and measurements are highly accurate.

Keywords: ball lens, quadrant detector, axial error, radial error

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Authors: Dimitris Varsamis, Nicholas Karampetakis

Abstract:

It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: bivariate interpolation polynomial, polynomial basis, transformations, interpolating polynomial

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Authors: Majid Rashidi, Shahrbanoo Farkhondeh Biabnavi

Abstract:

The hydrodynamic instability phenomenon in a journal bearing may occur by either a reduction in the load carried by journal bearing, by an increase in the journal speed, by change in the lubricant viscosity, or a combination of these factors. The previous research and development work done to overcome the instability issue of journal bearings, operating in hydrodynamic lubricate regime, can be categorized as follows: A) Actively controlling the bearing sleeve by using piezo actuator, b) Inclusion of strategically located and shaped internal grooves within inner surface of the bearing sleeve, c) Actively controlling the bearing sleeve using an electromagnetic actuator, d)Actively and externally pressurizing the lubricant within a journal bearing set, and e)Incorporating tilting pads within the inner surface of the bearing sleeve that assume different equilibrium angular position in response to changes in the bearing design parameter such as speed and load. This work presents an innovative design concept for a 'smart journal bearing' set to operate in a stable hydrodynamic lubrication regime, despite variations in bearing speed, load, and its lubricant viscosity. The proposed bearing design allows adjusting its radial clearance for an attempt to maintain a stable bearing operation under those conditions that may cause instability for a bearing with a fixed radial clearance. The design concept allows adjusting the radial clearance at small increments in the order of 0.00254 mm. This is achieved by axially moving two symmetric conical rigid cavities that are in close contact with the conically shaped outer shell of a sleeve bearing. The proposed work includes a 3D model of the bearing that depicts the structural interactions of the bearing components. The 3D model is employed to conduct finite element Analyses to simulate the mechanical behavior of the bearing from a structural point of view. The concept of controlling of the radial clearance, as presented in this work, is original and has not been proposed and discuss in previous research. A typical journal bearing was analyzed under a set of design parameters, namely r =1.27 cm (journal radius), c = 0.0254 mm (radial clearance), L=1.27 cm (bearing length), w = 445N (bearing load), μ = 0.028 Pascale (lubricant viscosity). A shaft speed as 3600 r.p.m was considered, and the mass supported by the bearing, m, is set to be 4.38kg. The Summerfield Number associated with the above bearing design parameters turn to be, S=0.3. These combinations resulted in stable bearing operation. Subsequently, the speed was postulated to increase from 3600 r.p.mto 7200 r.p.m; the bearing was found to be unstable under the new increased speed. In order to regain stability, the radial clearance was increased from c = 0.0254 mm to0.0358mm. The change in the radial clearance was shown to bring the bearing back to stable an operating condition.

Keywords: adjustable clearance, bearing, hydrodynamic, instability, journal

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Authors: Abdulmalek Ahmed

Abstract:

Formation pressure is the main function that affects drilling operation economically and efficiently. Knowing the pore pressure and the parameters that affect it will help to reduce the cost of drilling process. Many empirical models reported in the literature were used to calculate the formation pressure based on different parameters. Some of these models used only drilling parameters to estimate pore pressure. Other models predicted the formation pressure based on log data. All of these models required different trends such as normal or abnormal to predict the pore pressure. Few researchers applied artificial intelligence (AI) techniques to predict the formation pressure by only one method or a maximum of two methods of AI. The objective of this research is to predict the pore pressure based on both drilling parameters and log data namely; weight on bit, rotary speed, rate of penetration, mud weight, bulk density, porosity and delta sonic time. A real field data is used to predict the formation pressure using five different artificial intelligence (AI) methods such as; artificial neural networks (ANN), radial basis function (RBF), fuzzy logic (FL), support vector machine (SVM) and functional networks (FN). All AI tools were compared with different empirical models. AI methods estimated the formation pressure by a high accuracy (high correlation coefficient and low average absolute percentage error) and outperformed all previous. The advantage of the new technique is its simplicity, which represented from its estimation of pore pressure without the need of different trends as compared to other models which require a two different trend (normal or abnormal pressure). Moreover, by comparing the AI tools with each other, the results indicate that SVM has the advantage of pore pressure prediction by its fast processing speed and high performance (a high correlation coefficient of 0.997 and a low average absolute percentage error of 0.14%). In the end, a new empirical correlation for formation pressure was developed using ANN method that can estimate pore pressure with a high precision (correlation coefficient of 0.998 and average absolute percentage error of 0.17%).

Keywords: Artificial Intelligence (AI), Formation pressure, Artificial Neural Networks (ANN), Fuzzy Logic (FL), Support Vector Machine (SVM), Functional Networks (FN), Radial Basis Function (RBF)

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Authors: Kunpeng Wang, Hongchun, Wu, Liangzhi Cao, Chuanqi Zhao

Abstract:

The distributions of homogeneous neutron flux within a node were expanded into a set of analytic basis functions which satisfy the diffusion equation at any point in a triangular-z node for each energy group, and nodes were coupled with each other with both the zero- and first-order partial neutron current moments across all the interfaces of the triangular prism at the same time. Based this method, a code TABFEN has been developed and applied to solve the neutron diffusion equation in a complicated geometry. In addition, after a series of numerical derivation, one can get the neutron adjoint diffusion equations in matrix form which is the same with the neutron diffusion equation; therefore, it can be solved by TABFEN, and the low-high scan strategy is adopted to improve the efficiency. Four benchmark problems are tested by this method to verify its feasibility, the results show good agreement with the references which demonstrates the efficiency and feasibility of this method.

Keywords: analytic basis function expansion method, arbitrary triangular-z node, adjoint neutron flux, complicated geometry

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Authors: Haohao Wang

Abstract:

The purpose of this paper is to find elimination ideals via Grobner basis. We first introduce the concept of Grobner bases, and then, we provide computational algorithms to applications for curves and surfaces.

Keywords: curves, surfaces, Grobner basis, elimination

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Haoshu Li, Shaolong Wan

Abstract:

The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: Michal Geca, Grzegorz Baranski, Ksenia Siadkowska

Abstract:

The work is a part of the project which aims at developing innovative power and control systems for the high power aircraft piston engine ASz62IR. Developed electronically controlled ignition system will reduce emissions of toxic compounds as a result of lowered fuel consumption, optimized combustion and engine capability of efficient combustion of ecological fuels. The tested unit is an air-cooled four-stroke gasoline engine of 9 cylinders in a radial setup, mechanically charged by a radial compressor powered by the engine crankshaft. The total engine cubic capac-ity is 29.87 dm3, and the compression ratio is 6.4:1. The maximum take-off power is 1000 HP at 2200 rpm. The maximum fuel consumption is 280 kg/h. Engine powers aircrafts: An-2, M-18 „Dromader”, DHC-3 „OTTER”, DC-3 „Dakota”, GAF-125 „HAWK” i Y5. The main problems of the engine includes the imbalanced work of cylinders. The non-uniformity value in each cylinder results in non-uniformity of their work. In radial engine cylinders arrangement causes that the mixture movement that takes place in accordance (lower cylinder) or the opposite (upper cylinders) to the direction of gravity. Preliminary tests confirmed the presence of uneven workflow of individual cylinders. The phenomenon is most intense at low speed. The non-uniformity is visible on the waveform of cylinder pressure. Therefore two studies were conducted to determine the impact of this phenomenon on the engine performance: simulation and real tests. Simplified simulation was conducted on the element of the intake system coated with fuel film. The study shows that there is an effect of gravity on the movement of the fuel film inside the radial engine intake channels. Both in the lower and the upper inlet channels the film flows downwards. It follows from the fact that gravity assists the movement of the film in the lower cylinder channels and prevents the movement in the upper cylinder channels. Real tests on aircraft engine ASz62IR was conducted in transients condition (rapid change of the excess air in each cylinder were performed. Calculations were conducted for mass of fuel reaching the cylinders theoretically and really and on this basis, the factors of fuel evaporation “x” were determined. Therefore a simplified model of the fuel supply to cylinder was adopted. Model includes time constant of the fuel film τ, the number of engine transport cycles of non-evaporating fuel along the intake pipe γ and time between next cycles Δt. The calculation results of identification of the model parameters are presented in the form of radar graphs. The figures shows the averages declines and increases of the injection time and the average values for both types of stroke. These studies shown, that the change of the position of the cylinder will cause changes in the formation of fuel-air mixture and thus changes in the combustion process. Based on the results of the work of simulation and experiments was possible to develop individual algorithms for ignition control. This work has been financed by the Polish National Centre for Research and Development, INNOLOT, under Grant Agreement No. INNOLOT/I/1/NCBR/2013.

Keywords: radial engine, ignition system, non-uniformity, combustion process

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