Search results for: laplace homotopy perturbation method

Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

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The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: curved beam, dynamic analysis, elastic foundation, finite element method

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Authors: J. Jena, Monica Saxena

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In this paper, the propagation of weak nonlinear waves in non-equilibrium flow has been studied in detail using the perturbation method. The expansive action of receding piston undergoing infinite acceleration has been discussed. Central expansion fan, compression waves and shock fronts have been discussed and the solutions up to the first order in the characteristic plane and physical plane have been obtained.

Keywords: Characteristic wave front, weak non-linear waves, central expansion fan, compression waves

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Authors: Sebastian Andersen, Peter N. Poulsen

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The use of basis projection in the structural dynamic analysis is frequently applied. The purpose of the method is to improve the computational efficiency, while maintaining a high solution accuracy, by projection the governing equations onto a small set of carefully selected basis vectors. The present work considers basis projection in kinematic nonlinear systems with a focus on two widely used basis vectors; the system mode shapes and their modal derivatives. Particularly the latter basis vectors are given special attention since only approximate modal derivatives have been used until now. In the present work the complete modal derivatives, derived from perturbation methods, are presented and compared to the previously applied approximate modal derivatives. The correctness of the complete modal derivatives is illustrated by use of an example of a harmonically loaded kinematic nonlinear structure modeled by beam elements.

Keywords: basis projection, finite element method, kinematic nonlinearities, modal derivatives

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Yashar Haghighatfar, Shahrzad Mirhosseini

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Pull-in instability is a nonlinear and crucial effect that is important for the design of microelectromechanical system devices. In this paper, the appropriate electrostatic voltage range is determined by measuring fluid flow pressure via micro pressure sensor based microbeam. The microbeam deflection contains two parts, the static and perturbation deflection of static. The second order equation regarding the equivalent stiffness, mass and damping matrices based on Galerkin method is introduced to predict pull-in instability due to the external voltage. Also the reduced order method is used for solving the second order nonlinear equation of motion. Furthermore, in the present study, the micro capacitive pressure sensor is designed for measuring special fluid flow pressure range. The results show that the measurable pressure range can be optimized, regarding damping field and external voltage.

Keywords: MEMS, pull-in instability, electrostatically actuated microbeam, reduced order method

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Authors: Jack R. McKenzie, Peter A. Appleby, Thomas House, Neil Walton

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Cold-start is a notoriously difficult problem which can occur in recommendation systems, and arises when there is insufficient information to draw inferences for users or items. To address this challenge, a contextual bandit algorithm – the Fast Approximate Bayesian Contextual Cold Start Learning algorithm (FAB-COST) – is proposed, which is designed to provide improved accuracy compared to the traditionally used Laplace approximation in the logistic contextual bandit, while controlling both algorithmic complexity and computational cost. To this end, FAB-COST uses a combination of two moment projection variational methods: Expectation Propagation (EP), which performs well at the cold start, but becomes slow as the amount of data increases; and Assumed Density Filtering (ADF), which has slower growth of computational cost with data size but requires more data to obtain an acceptable level of accuracy. By switching from EP to ADF when the dataset becomes large, it is able to exploit their complementary strengths. The empirical justification for FAB-COST is presented, and systematically compared to other approaches on simulated data. In a benchmark against the Laplace approximation on real data consisting of over 670, 000 impressions from autotrader.co.uk, FAB-COST demonstrates at one point increase of over 16% in user clicks. On the basis of these results, it is argued that FAB-COST is likely to be an attractive approach to cold-start recommendation systems in a variety of contexts.

Keywords: cold-start learning, expectation propagation, multi-armed bandits, Thompson Sampling, variational inference

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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Authors: S. H. Iranmanesh, L. Aliabadi, A. Mollajan

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Integrated resilience engineering (IRE) is capable of returning banking systems to the normal state in extensive economic circumstances. In this study, information system of a large bank (with several branches) is assessed and optimized under severe economic conditions. Data envelopment analysis (DEA) models are employed to achieve the objective of this study. Nine IRE factors are considered to be the outputs, and a dummy variable is defined as the input of the DEA models. A standard questionnaire is designed and distributed among executive managers to be considered as the decision-making units (DMUs). Reliability and validity of the questionnaire is examined based on Cronbach's alpha and t-test. The most appropriate DEA model is determined based on average efficiency and normality test. It is shown that the proposed integrated design provides higher efficiency than the conventional RE design. Results of sensitivity and perturbation analysis indicate that self-organization, fault tolerance, and reporting culture respectively compose about 50 percent of total weight.

Keywords: banking system, Data Envelopment Analysis (DEA), Integrated Resilience Engineering (IRE), performance evaluation, perturbation analysis

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Authors: Marco Tulio C. Faria

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Fixed-geometry hydrodynamic journal bearings are one of the best supporting systems for several applications of rotating machinery. Cylindrical journal bearings present excellent load-carrying capacity and low manufacturing costs, but they are subjected to the oil-film instability at high speeds. An attempt of overcoming this instability problem has been the development of non-circular journal bearings. This work deals with an analysis of oil-lubricated elliptical journal bearings using the finite element method. Steady-state and dynamic performance characteristics of elliptical bearings are rendered by zeroth- and first-order lubrication equations obtained through a linearized perturbation method applied on the classical Reynolds equation. Four-node isoparametric rectangular finite elements are employed to model the bearing thin film flow. Curves of elliptical bearing load capacity and dynamic force coefficients are rendered at several operating conditions. The results presented in this work demonstrate the influence of the bearing ellipticity on its performance at different loading conditions.

Keywords: elliptical journal bearings, non-circular journal bearings, hydrodynamic bearings, finite element method

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Authors: Rasaq Kareem, Jacob Gbadeyan

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In this study, analysis of the entropy generation of an unsteady reactive hydromagnetic generalized couette fluid flow of a two-step exothermic chemical reaction through a channel with isothermal wall temperature under the influence of different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics was investigated. The modelled nonlinear dimensionless equations governing the fluid flow were simplified and solved using the combined Laplace Differential Transform Method (LDTM). The effects of fluid parameters associated with the problem on the fluid temperature, entropy generation rate and Bejan number were discussed and presented through graphs.

Keywords: couette, entropy, exothermic, unsteady

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Authors: Alemayehu Mengesha, Solomon Belay

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We determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in an astrophysical plasma by considering the effect of viscosity with an anisotropic pressure tensor. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of the dispersion relation equation. Our result indicates that an astrophysical plasma with an anisotropic pressure tensor is stable in the presence of viscosity and a strong magnetic field at considerable wavelength. Currently, we are doing the numerical analysis of this work.

Keywords: astrophysical, magnetic field, instability, MHD, wavelength, viscosity

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Authors: Jing Yu, Hongyang Liu, Dong Hao

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On-Orbit Refueling is of great significance in extending space crafts' lifetime. The problem of minimum-fuel, time-fixed, Peer-to-Peer On-Orbit Refueling mission planning is addressed here with the particular aim of assigning fuel-insufficient satellites to the fuel-sufficient satellites and optimizing each rendezvous trajectory. Constraints including perturbation, communication link, sun illumination, hold points for different rendezvous phases, and sensor switching are considered. A planning model has established as well as a two-level solution method. The upper level deals with target assignment based on fuel equilibrium criterion, while the lower level solves constrained trajectory optimization using special maneuver strategies. Simulations show that the developed method could effectively resolve the Peer-to-Peer On-Orbit Refueling mission planning problem and deal with complex constraints.

Keywords: mission planning, orbital rendezvous, on-orbit refueling, space mission

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Authors: Abdennour Benmakhlouf, Abdelouahab Bentabet

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In this paper, we investigated the athermal pressure behavior of the structural and elastic properties of scheelite BaWO4 phase up to 7 GPa using the ab initio pseudo-potential method. The calculated lattice parameters pressure relation have been compared with the experimental values and found to be in good agreement with these results. Moreover, we present for the first time the investigation of the elastic properties of this compound using the density functional perturbation theory (DFPT). It is shown that this phase is mechanically stable up to 7 GPa after analyzing the calculated elastic constants. Other relevant quantities such as bulk modulus, pressure derivative of bulk modulus, shear modulus; Young’s modulus, Poisson’s ratio, anisotropy factors, Debye temperature and sound velocity have been calculated. The obtained results, which are reported for the first time to the best of the author’s knowledge, can facilitate assessment of possible applications of the title material.

Keywords: pseudo-potential method, pressure, structural and elastic properties, scheelite BaWO4 phase

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Authors: Aaron Aboshio, Jianqiao Ye

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In this study, static and dynamic responses of a typical reinforced concrete flat slab, designed to British Standard (BS 8110, 1997) and under self and live loadings for dance halls are reported. Linear perturbation analysis using finite element method was employed for modal, impulse loading and frequency response analyses of the slab under the aforementioned loading condition. Results from the static and dynamic analyses, comprising of the slab fundamental frequencies and mode shapes, dynamic amplification factor, maximum deflection, stress distributions among other valuable outcomes are presented and discussed. These were gauged with the limiting provisions in the design code with a view to optimise the structure and ensure both adequate strength and economical section for large clear span slabs. This is necessary owing to the continued increase in cost of erecting building structures and the squeeze on public finance globally.

Keywords: economical design, finite element method, modal dynamics, reinforced concrete, slab

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Authors: R. Whalley

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The heat transfer modelling for a diffusion process will be considered. Difficulties in computing the time-distance dynamics of the representation will be addressed. Incomplete and irrational Laplace function will be identified as the computational issue. Alternative approaches to the response evaluation process will be provided. An illustration application problem will be presented. Graphical results confirming the theoretical procedures employed will be provided.

Keywords: heat, transfer, diffusion, modelling, computation

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Authors: Shashi Sharma, Uaday Singh, V. K. Katiyar

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Blood flow through a stenosed tube, which is of great interest to mechanical engineers as well as medical researchers. If stenosis exists in an artery, normal blood flow is disturbed. The deposition of fatty substances, cholesterol, cellular waste products in the inner lining of an artery results to plaque formation .The present study deals with a mathematical model for blood flow in constricted arteries. Blood is considered as a Newtonian, incompressible, unsteady and laminar fluid flowing in a cylindrical rigid tube along the axial direction. A time varying pressure gradient is applied in the axial direction. An analytical solution is obtained using the numerical inversion method for Laplace Transform for calculating the velocity profile of fluid as well as particles.

Keywords: blood flow, stenosis, Newtonian fluid, medical biology and genetics

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Authors: Y. M. Aiyesimi, G. T. Okedayo, O. W. Lawal

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The analysis has been carried out to study unsteady MHD thin film flow of a third grade fluid down an inclined plane with heat transfer when the slippage between the surface of plane and the lower surface of the fluid is valid. The governing nonlinear partial differential equations involved are reduced to linear partial differential equations using regular perturbation method. The resulting equations were solved analytically using method of separation of variable and eigenfunctions expansion. The solutions obtained were examined and discussed graphically. It is interesting to find that the variation of the velocity and temperature profile with the slip and magnetic field parameter depends on time.

Keywords: non-Newtonian fluid, MHD flow, thin film flow, third grade fluid, slip boundary condition, heat transfer, separation of variable, eigenfunction expansion

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Authors: Nadeem Bashir, Ghulam Mustafa Peerzada

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The present study pertains to the nonlinear behavior of acetaminophen based uncatalyzed Belousov-Zhabotinsky (BZ) oscillator and its dynamics in the presence of Ferroin as the catalyst. The role of free metal ions as catalysts was examined and the results compared with corresponding complexed catalysts. Free metal ions were found to be sluggish with respect to the evolution of the oscillatory regime as compared to complexed ones. Effect of change of the ligand moiety of the catalyst complex on the oscillatory parameters was monitored. Since ethanol potentiates the hepatotoxicity caused by acetaminophen in-vivo, it is thought to understand this interaction by virtue of causing perturbation of the acetaminophen based oscillator with different concentrations of the ethanol with and without ferroin as the catalyst. Another dimension to the ethanol effect was added by perturbation of the system with ethanol at different stages of the reaction so as to get an idea whether it is acetaminophen or some reactive intermediate generated in the reaction system which reacts with ethanol. Further, the ferroin-catalyzed oscillator is taken as a prototype inorganic model of the acetaminophen-ethanol syndrome, as ferroin and HOBr were inorganic replacements to Cyt P450 and NADPH in the alcohol metabolism.

Keywords: Belousov-Zhabotinsky reaction, ferroin, Paracetamol-Ethanol syndrome, kinetics

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Authors: X. Li, Y. Liu, H. Wong, B. Pardoen, A. Fabbri, F. McGregor, E. Liu

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The target of this paper is to investigate how saturated poroelastic soils subject to freezing temperatures behave and how different boundary conditions can intervene and affect the thermo-hydro-mechanical (THM) responses, based on a particular but classical configuration of a finite homogeneous soil layer studied by Terzaghi. The essential relations on the constitutive behavior of a freezing soil are firstly recalled: ice crystal - liquid water thermodynamic equilibrium, hydromechanical constitutive equations, momentum balance, water mass balance, and the thermal diffusion equation, in general, non-linear case where material parameters are state-dependent. The system of equations is firstly linearized, assuming all material parameters to be constants, particularly the permeability of liquid water, which should depend on the ice content. Two analytical solutions solved by the classic Laplace transform are then developed, accounting for two different sets of boundary conditions. Afterward, the general non-linear equations with state-dependent parameters are solved using a commercial code COMSOL based on finite elements method to obtain numerical results. The validity of this numerical modeling is partially verified using the analytical solution in the limiting case of state-independent parameters. Comparison between the results given by the linearized analytical solutions and the non-linear numerical model reveals that the above-mentioned linear computation will always underestimate the liquid pore pressure and displacement, whatever the hydraulic boundary conditions are. In the nonlinear model, the faster growth of ice crystals, accompanying the subsequent reduction of permeability of freezing soil layer, makes a longer duration for the depressurization of water liquid and slower settlement in the case where the ground surface is swiftly covered by a thin layer of ice, as well as a bigger global liquid pressure and swelling in the case of the impermeable ground surface. Nonetheless, the analytical solutions based on linearized equations give a correct order-of-magnitude estimate, especially at moderate temperature variations, and remain a useful tool for preliminary design checks.

Keywords: chemical potential, cryosuction, Laplace transform, multiphysics coupling, phase transformation, thermodynamic equilibrium

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Authors: Orhun Aydin, Mark V. Janikas, Rodrigo Alves, Renato Assuncao

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In this paper, a tree-based perturbation methodology for regionalization inference is presented. Regionalization is a constrained optimization problem that aims to create groups with similar attributes while satisfying spatial contiguity constraints. Similar to any constrained optimization problem, the spatial constraint may hinder convergence to some global minima, resulting in spatially contiguous members of a group with dissimilar attributes. This paper presents a general methodology for rigorously perturbing spatial constraints through the use of random spanning trees. The general framework presented can be used to quantify the effect of the spatial constraints in the overall regionalization result. We compare several types of stochastic spanning trees used in inference problems such as fuzzy regionalization and determining the number of regions. Performance of stochastic spanning trees is juxtaposed against the traditional permutation-based hypothesis testing frequently used in spatial statistics. Inference results for fuzzy regionalization and determining the number of regions is presented on the Local Area Personal Incomes for Texas Counties provided by the Bureau of Economic Analysis.

Keywords: regionalization, constrained clustering, probabilistic inference, fuzzy clustering

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Authors: Ahmad K. Samaila, Basant K. Jha

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This study is devoted to investigate the effect of transpiration on transient as well as steady-state natural convection flow of a reactive viscous fluid in a vertical channel formed by two infinite vertical parallel porous plates. The Boussinesq assumption is applied and the nonlinear governing equations of energy and momentum are developed. The problem is solved numerically using implicit finite difference method and analytically for steady-state case using perturbation method. Solutions are presented in graphical form for fluid temperature, velocity, and skin-friction and wall heat transfer rate for various parametric values. It is found that velocity, temperature, rate of heat transfer as well as skin-friction are strongly affected by mass leakage through the porous plates.

Keywords: transpiration, reactive viscous fluid, porous plates, natural convection, suction/injection

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Authors: Aicha Rima Cheniti, Hatem Besbes, Joseph Haggege, Christophe Sintes

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In this paper, we are interested to determine the carbon dioxide pressure in the arterial blood through radial velocity difference. The blood was modeled as a two phase mixture (an aqueous carbon dioxide solution with carbon dioxide gas) by Drift flux model and the Young-Laplace equation. The distributions of mixture velocities determined from the considered model permitted the calculation of the radial velocity distributions with different values of mean mixture pressure and the calculation of the mean carbon dioxide pressure knowing the mean mixture pressure. The radial velocity distributions are used to deduce a calculation method of the mean mixture pressure through the radial velocity difference between two positions which is measured by ultrasound. The mean carbon dioxide pressure is then deduced from the mean mixture pressure.

Keywords: mean carbon dioxide pressure, mean mixture pressure, mixture velocity, radial velocity difference

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Authors: Najrullah Khan, Athar Ali Khan

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The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

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Authors: M. Samadzadeh Mahabadi, J. Shanbehzadeh

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This paper presents a hybrid digital image-watermarking scheme, which is robust against varieties of attacks and geometric distortions. The image content is represented by important feature points obtained by an image-texture-based adaptive Harris corner detector. These feature points are extracted from LL2 of 2-D discrete wavelet transform which are obtained by using the Harris-Laplacian detector. We calculate the Fourier transform of circular regions around these points. The amplitude of this transform is rotation invariant. The experimental results demonstrate the robustness of the proposed method against the geometric distortions and various common image processing operations such as JPEG compression, colour reduction, Gaussian filtering, median filtering, and rotation.

Keywords: digital watermarking, geometric distortions, geometrical attack, Harris Laplace, important feature points, rotation, scale invariant feature

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Authors: Sanjit Kumar Paul, A. A. Mamun, M. R. Amin

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The Linear propagation of the dust-acoustic wave in a dusty plasma consisting of Boltzmann distributed electrons and ions and mobile charge fluctuating positive dust grains has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and its responsible for the formation of the dust-acoustic waves in such a dusty plasma. The basic features of such dust-acoustic waves have been identified. It has been proposed to design a new laboratory experiment which will be able to identify the basic features of the dust-acoustic waves predicted in this theoretical investigation.

Keywords: dust acoustic waves, dusty plasma, Boltzmann distributed electrons, charge fluctuation

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Authors: Tugrul Oktay, Mehmet Konar, Mustafa Soylak, Firat Sal, Murat Onay, Orhan Kizilkaya

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In this paper, autonomous performance of a small manufactured unmanned helicopter is tried to be increased. For this purpose, a small unmanned helicopter is manufactured in Erciyes University, Faculty of Aeronautics and Astronautics. It is called as ZANKA-Heli-I. For performance maximization, autopilot parameters are determined via minimizing a cost function consisting of flight performance parameters such as settling time, rise time, overshoot during trajectory tracking. For this purpose, a stochastic optimization method named as simultaneous perturbation stochastic approximation is benefited. Using this approach, considerable autonomous performance increase (around %23) is obtained.

Keywords: small helicopters, hierarchical control, stochastic optimization, autonomous performance maximization, autopilots

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Authors: James Jr. Mashiyane, Risuna Nkolele, Stephanie J. Müller, Gciniwe S. Dlamini, Rebone L. Meraba, Darlington S. Mapiye

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When performing language tasks in natural language processing (NLP), the dimensionality of word embeddings is chosen either ad-hoc or is calculated by optimizing the Pairwise Inner Product (PIP) loss. The PIP loss is a metric that measures the dissimilarity between word embeddings, and it is obtained through matrix perturbation theory by utilizing the unitary invariance of word embeddings. Unlike in natural language, in genomics, especially in genome sequence processing, unlike in natural language processing, there is no notion of a “word,” but rather, there are sequence substrings of length k called k-mers. K-mers sizes matter, and they vary depending on the goal of the task at hand. The dimensionality of word embeddings in NLP has been studied using the matrix perturbation theory and the PIP loss. In this paper, the sufficiency and reliability of applying word-embedding algorithms to various genomic sequence datasets are investigated to understand the relationship between the k-mer size and their embedding dimension. This is completed by studying the scaling capability of three embedding algorithms, namely Latent Semantic analysis (LSA), Word2Vec, and Global Vectors (GloVe), with respect to the k-mer size. Utilising the PIP loss as a metric to train embeddings on different datasets, we also show that Word2Vec outperforms LSA and GloVe in accurate computing embeddings as both the k-mer size and vocabulary increase. Finally, the shortcomings of natural language processing embedding algorithms in performing genomic tasks are discussed.

Keywords: word embeddings, k-mer embedding, dimensionality reduction

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis

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Authors: Khalid. M. O. Elmabrok, M. L. Burby, G. G. Nasr

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Flow instability during gas lift operation is caused by three major phenomena – the density wave oscillation, the casing heading pressure and the flow perturbation within the two-phase flow region. This paper focuses on the causes and the effect of flow instability during gas lift operation and suggests ways to control it in order to maximise productivity during gas lift operations. A laboratory-scale two-phase flow system to study the effects of flow perturbation was designed and built. The apparatus is comprised of a 2 m long by 66 mm ID transparent PVC pipe with air injection point situated at 0.1 m above the base of the pipe. This is the point where stabilised bubbles were visibly clear after injection. Air is injected into the water filled transparent pipe at different flow rates and pressures. The behavior of the different sizes of the bubbles generated within the two-phase region was captured using a digital camera and the images were analysed using the advanced image processing package. It was observed that the average maximum bubbles sizes increased with the increase in the length of the vertical pipe column from 29.72 to 47 mm. The increase in air injection pressure from 0.5 to 3 bars increased the bubble sizes from 29.72 mm to 44.17 mm and then decreasing when the pressure reaches 4 bars. It was observed that at higher bubble velocity of 6.7 m/s, larger diameter bubbles coalesce and burst due to high agitation and collision with each other. This collapse of the bubbles causes pressure drop and reverse flow within two phase flow and is the main cause of the flow instability phenomena.

Keywords: gas lift instability, bubbles forming, bubbles collapsing, image processing

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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