Search results for: differential cross section

Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Mengke Zhan, Cheng-Gang Xie, Jian-Jun Shu

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A venturi flowmeter is a common device used in multiphase flow rate measurement in the upstream oil and gas industry. Having a robust computational model for multiphase flow in a venturi is desirable for understanding the gas-liquid and fluid-pipe interactions and predicting pressure and phase distributions under various flow conditions. A steady Eulerian-Eulerian framework is used to simulate upward gas-liquid flow in a vertical venturi. The simulation results are compared with experimental measurements of venturi differential pressure and chord-averaged gas holdup in the venturi throat section. The choice of turbulence model is nontrivial in the multiphase flow modelling in a venturi. The performance cross-comparison of the k-ϵ model, Reynolds stress model (RSM) and shear-stress transport (SST) k-ω turbulence model is made in the study. In terms of accuracy and computational cost, the SST k-ω turbulence model is observed to be the most efficient.

Keywords: computational fluid dynamics (CFD), gas-liquid flow, turbulence modelling, venturi

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Andreea Halunga, Chris D. Orme, Takashi Yamagata

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This paper proposes a heteroskedasticity-robust Breusch-Pagan test of the null hypothesis of zero cross-section (or contemporaneous) correlation in linear panel-data models, without necessarily assuming independence of the cross-sections. The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution. The asymptotic validity of the test procedure is predicated on the number of time series observations, T, being large relative to the number of cross-section units, N, in that: (i) either N is fixed as T→∞; or, (ii) N²/T→0, as both T and N diverge, jointly, to infinity. Given this, it is not expected that asymptotic theory would provide an adequate guide to finite sample performance when T/N is "small". Because of this, we also propose and establish asymptotic validity of, a number of wild bootstrap schemes designed to provide improved inference when T/N is small. Across a variety of experimental designs, a Monte Carlo study suggests that the predictions from asymptotic theory do, in fact, provide a good guide to the finite sample behaviour of the test when T is large relative to N. However, when T and N are of similar orders of magnitude, discrepancies between the nominal and empirical significance levels occur as predicted by the first-order asymptotic analysis. On the other hand, for all the experimental designs, the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels, when T/N is small, with a recursive-design wild bootstrap scheme performing best, in general, and providing quite close agreement between the nominal and empirical significance levels of the test even when T and N are of similar size. Moreover, in comparison with the wild bootstrap "version" of the original Breusch-Pagan test our experiments indicate that the corresponding version of the heteroskedasticity-robust Breusch-Pagan test appears reliable. As an illustration, the proposed tests are applied to a dynamic growth model for a panel of 20 OECD countries.

Keywords: cross-section correlation, time-series heteroskedasticity, dynamic panel data, heteroskedasticity robust Breusch-Pagan test

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Authors: Gokhan Dok, Hakan Ozturk, Aydin Demir

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The behavior of reinforced concrete (RC) members is quite important in RC structures. When evaluating the performance of structures, the nonlinear properties are defined according to the cross sectional behavior of RC members. To be able to determine the behavior of RC members, its cross sectional behavior should be known well. The moment-curvature (MC) relationship is used to represent cross sectional behavior. The MC relationship of RC cross section can be best determined both experimentally and numerically. But, experimental study on RC members is very difficult. The aim of the study is to obtain the MC relationship of RC shear walls. Additionally, it is aimed to determine the parameters which affect MC relationship. While obtaining MC relationship of RC members, XTRACT which can represent robustly the MC relationship is used. Concrete quality, longitudinal and transverse reinforcing ratios, are selected as parameters which affect MC relationship. As a result of the study, curvature ductility and effective flexural stiffness are determined using this parameter. Effective flexural stiffness is compared with the values defined in design codes.

Keywords: moment-curvature, reinforced concrete, shear wall, numerical

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Qiang Zhang, Xiaojian Hu

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Aiming at the problem of the existing real-time evaluation methods for traffic safety status, a video information-based urban road section traffic safety status evaluation method was established, and the rapid detection method of traffic flow parameters based on video information is analyzed. The concept of the speed dispersion of the road section that affects the traffic safety state of the urban road section is proposed, and the method of evaluating the traffic safety state of the urban road section based on the speed dispersion of the road section is established. Experiments show that the proposed method can reasonably evaluate the safety status of urban roads in real-time, and the evaluation results can provide a corresponding basis for the traffic management department to formulate an effective urban road section traffic safety improvement plan.

Keywords: intelligent transportation system, road traffic safety, video information, vehicle speed dispersion

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Authors: Thulodin Mat Lazim, Aminuddin Saat, Ammar Fakhir Abdulwahid, Zaid Sattar Kareem

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Film cooling is one of the cooling systems investigated for the application to gas turbine blades. Gas turbines use film cooling in addition to turbulence internal cooling to protect the blades outer surface from hot gases. The present study concentrates on the numerical investigation of film cooling performance for a row of twisted cylindrical holes in modern turbine blade. The adiabatic film effectiveness and the heat transfer coefficient are determined numerical on a flat plate downstream of a row of inclined different cross section area hole exit by using Computational Fluid Dynamics (CFD). The swirling motion of the film coolant was induced the twisted angle of film cooling holes, which inclined an angle of α toward the vertical direction and surface of blade turbine. The holes angle α of the impingement mainstream was changed from 90°, 65°, 45°, 30° and 20°. The film cooling effectiveness on surface of blade turbine wall was measured by using 3D Computational Fluid Dynamics (CFD). Results showed that the effectiveness of rectangular twisted hole has the effectiveness among other cross section area of the hole at blowing ratio (0.5, 1, 1.5 and 2).

Keywords: turbine blade cooling, film cooling, geometry shape of hole, turbulent flow

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Rahal Nacer, Beghdad Houda, Tehami Mohamed, Souici Abdelaziz

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Although the shrinkage of the concrete causes undesirable parasitic effects to the structure, it can then harm the resistance and the good appearance of the structure. Long term behaviourmodelling of steel-concrete composite beams requires the use of the time variable and the taking into account of all the sustained stress history of the concrete slab constituting the cross section. The work introduced in this article is a theoretical study of the behaviour of composite beams with respect to the phenomenon of concrete shrinkage. While using the theory of the linear viscoelasticity of the concrete, and on the basis of the rate of creep method, in proposing an analytical model, made up by a system of two linear differential equations, emphasizing the effects caused by shrinkage on the resistance of a steel-concrete composite beams. Results obtained from the application of the suggested model to a steel-concrete composite beam are satisfactory.

Keywords: composite beams, shrinkage, time, rate of creep method, viscoelasticity theory

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Authors: Harshavardhan Reddy, Balaji Subramanian

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A systematic parametric study to find the optimum bellmouth profile by relating geometric and performance parameters to satisfy a set of specifications is reported. A careful aerodynamic design of bellmouth intake is critical to properly direct the flow with minimal losses and maximal flow uniformity into the honeycomb located inside the settling chamber of an indraft wind tunnel, thus improving the efficiency of the entire unit. Design charts for elliptically profiled bellmouths with two different contraction ratios (9 and 18) and three different test section speeds (25 m/s, 50 m/s, and 75 m/s) were presented. A significant performance improvement - especially in the Coefficient of discharge and in the flow angularity and boundary layer thickness at the honeycomb inlet - was observed when an entry corner radius (r/D = 0.08) was added to the bellmouth profile. The nonuniformity at the honeycomb inlet drops by about three times (~1% to 0.3%) when moving from square to regular octagonal cross-section. An octagonal cross-sectioned bellmouth intake with L/d = 0.55, D/d = 1.625, and r/D = 0.08 met all the four target performance specifications and is proposed as the best choice for a low-speed wind tunnel.

Keywords: bellmouth intake, low-speed wind tunnel, coefficient of discharge, nonuniformity, flow angularity, boundary layer thickness, CFD, aerodynamics

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Zhan Chen, Wenquan Bi

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This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Katherine Russell

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Background: Over recent decades the number of caesarean sections performed in the UK has continued to rise. The cause of the rising caesarean rate (CSR) is not well understood. However, one of the most heavily cited reasons is an increase in maternal request for caesarean section. Maternal request for caesarean section (CDMR) refers to a caesarean section performed on maternal request with no medical indication. The true rate of caesarean delivery on maternal request in the UK and its contribution to the caesarean section rate is not known. Methods: To elucidate current understanding of the cause of the rising caesarean section rate and the role of CDMR we conducted a systematic review of the literature. To determine the role of CDMR in the CSR at the PRH we conducted a retrospective observational study of the caesarean section rates and CDMR from 2009-2015. Results: We demonstrated a negative correlation between rates of elective sections and CDMR over the study period (-0.123). On average, there were more elective sections performed after 2011 (15.10% of all deliveries) than before 2011 (12.41% of all deliveries); this difference was statistically significant (p = < 0.001). There were more cases of CDMR after 2011 (1.39% of all deliveries) than before 2011 (0.85% of all deliveries). The difference in average rates of CDMR before and after 2011 was statistically significant (p ≤ 0.001). Conclusions: CDMR is only a minor contributor to the CSR at the PRH. However, it remains an important factor because it represents a target for the reduction of the CSR that is more manageable than other, more complex and ubiquitous causes of the rising CSR.

Keywords: cesarean section, maternal request for cesarean section, obstetrics, pre-natal health

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Robert Pečenko, Karin Tomažič, Igor Planinc, Sabina Huč, Tomaž Hozjan

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Timber is favourable structural material due to high strength to weight ratio, recycling possibilities, and green credentials. Despite being flammable material, it has relatively high fire resistance. Everyday engineering practice around the word is based on an outdated design of timber structures considering standard fire exposure, while modern principles of performance-based design enable use of advanced non-standard fire curves. In Europe, standard for fire design of timber structures EN 1995-1-2 (Eurocode 5) gives two methods, reduced material properties method and reduced cross-section method. In the latter, fire resistance of structural elements depends on the effective cross-section that is a residual cross-section of uncharred timber reduced additionally by so called zero strength layer. In case of standard fire exposure, Eurocode 5 gives a fixed value of zero strength layer, i.e. 7 mm, while for non-standard parametric fires no additional comments or recommendations for zero strength layer are given. Thus designers often implement adopted 7 mm rule also for parametric fire exposure. Since the latest scientific evidence suggests that proposed value of zero strength layer can be on unsafe side for standard fire exposure, its use in the case of a parametric fire is also highly questionable and more numerical and experimental research in this field is needed. Therefore, the purpose of the presented study is to use advanced calculation methods to investigate the thickness of zero strength layer and parametric charring rates used in effective cross-section method in case of parametric fire. Parametric studies are carried out on a simple solid timber beam that is exposed to a larger number of parametric fire curves Zero strength layer and charring rates are determined based on the numerical simulations which are performed by the recently developed advanced two step computational model. The first step comprises of hygro-thermal model which predicts the temperature, moisture and char depth development and takes into account different initial moisture states of timber. In the second step, the response of timber beam simultaneously exposed to mechanical and fire load is determined. The mechanical model is based on the Reissner’s kinematically exact beam model and accounts for the membrane, shear and flexural deformations of the beam. Further on, material non-linear and temperature dependent behaviour is considered. In the two step model, the char front temperature is, according to Eurocode 5, assumed to have a fixed temperature of around 300°C. Based on performed study and observations, improved levels of charring rates and new thickness of zero strength layer in case of parametric fires are determined. Thus, the reduced cross section method is substantially improved to offer practical recommendations for designing fire resistance of timber structures. Furthermore, correlations between zero strength layer thickness and key input parameters of the parametric fire curve (for instance, opening factor, fire load, etc.) are given, representing a guideline for a more detailed numerical and also experimental research in the future.

Keywords: advanced numerical modelling, parametric fire exposure, timber structures, zero strength layer

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Authors: Yibeltal T. Bayou, Yohana S. Mashalla, Gloria Thupayagale-Tshweneagae

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Background: According to the World Health Organization, caesarean section delivery rates of more than 10-15% caesarean section deliveries in any specific geographic region in the world are not justifiable. The aim of the study was to describe the level and analyse determinants of caesarean section delivery in Addis Ababa. Methods: Data was collected in Addis Ababa using a structured questionnaire administered to 901 women aged 15-49 years through a stratified two-stage cluster sampling technique. Binary logistic regression model was employed to identify predictors of caesarean section delivery. Results: Among the 835 women who delivered their last birth at healthcare facilities, 19.2% of them gave birth by caesarean section. About 9.0% of the caesarean section births were due to mother’s request or service provider’s influence without any medical indication. The caesarean section delivery rate was much higher than the recommended rate particularly among the non-slum residents (27.2%); clients of private healthcare facilities (41.1%); currently married women (20.6%); women with secondary (22.2%) and tertiary (33.6%) level of education; and women belonging to the highest wealth quintile household (28.2%). The majority (65.8%) of the caesarean section clients were not informed about the consequences of caesarean section delivery by service providers. The logistic regression model shows that older age (30-49), secondary and above education, non-slum residence, high-risk pregnancy and receiving adequate antenatal care were significantly positively associated with caesarean section delivery. Conclusion: Despite the unreserved effort towards achieving MDG 5 through safe skilled delivery assistance among others, the high caesarean section rate beyond the recommend limit, and the finding that caesarean sections done without medical indications were also alarming. The government and city administration should take appropriate measures before the problems become setbacks in healthcare provision. Further investigations should focus on the effect of caesarean section delivery on maternal and child health outcomes in the study area.

Keywords: Addis Ababa, caesarean section, mode of delivery, slum residence

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Authors: Shagil Akhtar, Syed Muneeb Iqbal, Mohammed R. Rahim

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Common steel tubes with similar confines were used in simulation of tubes with distinctive type of corrugated sections. These corrugated cross-sections were arc-tangent, triangular, trapezoidal and square corrugated sections. The outcome of fluctuating structures of tube cross-section shape on the deformation feedback, collapse form and energy absorption characteristics of tubes under quasi-static axial compression have been prepared numerically. The finite element package of ANSYS Workbench was applied in the current analysis. The axial load-displacement products accompanied by the fold formation of disparate tubes were inspected and compared. Deviation of the initial peak load and the mean crushing force of the tubes with distinctive cross-sections were conscientiously examined.

Keywords: absorbed energy, axial loading, corrugated tubes, finite element, initial peak load, mean crushing force

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Authors: Chul Park, Youngseok Kim, Sangsik Choi

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This study developed an electric jig for underwater structure inspection in order to solve the problem of the application of side scan sonar to underwater inspection, and analyzed correlations of empirical data in order to enhance sonar data resolution. For the application of tow-typed sonar to underwater structure inspection, an electric jig was developed. In fact, it was difficult to inspect a cross-section at the time of inspection with tow-typed equipment. With the development of the electric jig for underwater structure inspection, it was possible to shorten an inspection time over 20%, compared to conventional tow-typed side scan sonar, and to inspect a proper cross-section through accurate angle control. The indoor test conducted to enhance sonar data resolution proved that a water depth, the distance from an underwater structure, and a filming angle influenced a resolution and data quality. Based on the data accumulated through field experience, multiple regression analysis was conducted on correlations between three variables. As a result, the relational equation of sonar operation according to a water depth was drawn.

Keywords: underwater structure, SONAR, safety inspection, resolution

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Yue Zhang, Bo Yang, Gang Xiong, Mohamed Elchalakanic, Shidong Nie

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This study aims to investigate the lateral torsional buckling of I-shaped cross-section beams fabricated from Q460GJ structural steel plates. Both experimental and numerical simulation results are presented in this paper. A total of eight specimens were tested under a three-point bending, and the corresponding numerical models were established to conduct parametric studies. The effects of some key parameters such as the non-dimensional member slenderness and the height-to-width ratio, were investigated based on the verified numerical models. Also, the results obtained from the parametric studies were compared with the predictions calculated by different design codes including the Chinese design code (GB50017-2003, 2003), the new draft version of Chinese design code (GB50017-201X, 2012), Eurocode 3 (EC3, 2005) and the North America design code (ANSI/AISC360-10, 2010). These comparisons indicated that the sectional height-to-width ratio does not play an important role to influence the overall stability load-carrying capacity of Q460GJ structural steel beams with welded I-shaped cross-sections. It was also found that the design methods in GB50017-2003 and ANSI/AISC360-10 overestimate the overall stability and load-carrying capacity of Q460GJ welded I-shaped cross-section beams.

Keywords: experimental study, finite element analysis, global stability, lateral torsional buckling, Q460GJ structural steel

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Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: Abdulbaset Saad, Adel Younis, Zuomin Dong

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For design optimization with high-dimensional expensive problems, an effective and efficient optimization methodology is desired. This work proposes a series of modification to the Differential Evolution (DE) algorithm for solving computation Intensive Black-Box Problems. The proposed methodology is called Radial Basis Meta-Model Algorithm Assisted Differential Evolutionary (RBF-DE), which is a global optimization algorithm based on the meta-modeling techniques. A meta-modeling assisted DE is proposed to solve computationally expensive optimization problems. The Radial Basis Function (RBF) model is used as a surrogate model to approximate the expensive objective function, while DE employs a mechanism to dynamically select the best performing combination of parameters such as differential rate, cross over probability, and population size. The proposed algorithm is tested on benchmark functions and real life practical applications and problems. The test results demonstrate that the proposed algorithm is promising and performs well compared to other optimization algorithms. The proposed algorithm is capable of converging to acceptable and good solutions in terms of accuracy, number of evaluations, and time needed to converge.

Keywords: differential evolution, engineering design, expensive computations, meta-modeling, radial basis function, optimization

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Authors: Katerina Kormusheva

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Pricing plays a pivotal role in the marketing discipline as it directly influences consumer perceptions, purchase decisions, and overall market positioning of a product or service. This paper seeks to expand current knowledge in the area of discriminatory and differential pricing, a main area of marketing research. The methodology includes developing a framework and a model for determining how many price points to implement in differential pricing. We focus on choosing the levels of differentiation, derive a function form of the model framework proposed, and lastly, test it empirically with data from a large-scale marketing pricing experiment of services in telecommunications.

Keywords: marketing, differential pricing, price points, optimization

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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: Palash Dey, Sudip Talukdar

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In this work, a cross-breed approach is presented for obtaining both the amount of the damage intensity and location of damage existing in thin-walled members. This cross-breed approach is developed based on response surface methodology (RSM) and genetic algorithm (GA). Theoretical finite element (FE) model of cracked angle section thin walled curved beam has been linked to the developed approach to carry out trial experiments to generate response surface functions (RSFs) of free, forced and heterogeneous dynamic response data. Subsequently, the error between the computed response surface functions and measured dynamic response data has been minimized using GA to find out the optimum damage parameters (amount of the damage intensity and location). A single crack of varying location and depth has been considered in this study. The presented approach has been found to reveal good accuracy in prediction of crack parameters and possess great potential in crack detection as it requires only the current response of a cracked beam.

Keywords: damage parameters, finite element, genetic algorithm, response surface methodology, thin walled curved beam

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