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• Effect of viscosity ratio on bubble dynamics in shear-thinning liquid is studied. • For small rheological index, rising viscosity ratio makes bubble shape complex. • For large characteristic time, rising viscosity ratio makes bubble shape complex. • Appearance of viscosity blind region decreases bubble rise velocity at large time. • Mechanism of bubble unsteady deformation is analyzed in detail. The volume of fluid method combined with the adaptive grid method is used to study the influence of shear-thinning liquid viscosity ratio (ε) for various values of rheological index (n) and characteristic time (λ) on bubble shape, rise velocity, and apparent viscosity around a bubble; where 1/ λ represents the shear rate at which the change in the viscosity curve occurs from the low shear rate to the power-law region. The results show that, depending on the magnitudes of n and λ , the bubble shape and deformation parameter are strongly related to ε , and bubble shape can exhibit both stable and unstable states. There are two types of deformation phenomena for the unsteady deformation of bubbles. First, the aspect ratio changes with time, whereas the shape remains similar throughout. Second, the shape changes periodically with time. For the given values of n and λ , the bubble rise velocity at large time shows a nonlinear increase as ε increases from 10 to ∞. Under the conditions of n ≤ 0.3, λ* ≥ 68.6, and ε ≥ 100 (λ* is the dimensionless characteristic time), a viscosity blind region (a region of high viscosity, where ε is close to 1) appears behind the bubble. The tendency for the viscosity blind region is to reduce the bubble rise velocity at large time. [ABSTRACT FROM AUTHOR]

• A computationally efficient model for detailed mass and heat transfer is presented. • Even for bubble collapse, homobaricity and equilibrium assumptions remain valid. • Temporal and spatial resolution of transport processes reveal detailed flow physics. • Bubble dynamics, mass and heat transfer occur in a time-shifted and non-linear way. A mathematical model for the simulation of the dynamics of spherical vapor-air bubbles and its numerical implementation is presented. Heat and mass transfer and phase transition in terms of evaporation and condensation as well as air absorption and desorption are considered. Flow variables are discretized by a mixed finite volume / finite difference scheme and solved either by a Crank-Nicolson or Runge-Kutta scheme. Due to the assumption of homogeneous bubble pressure (homobaricity), the solution of momentum equations is restricted to the Rayleigh-Plesset equation which makes the model computationally efficient. The model is validated by measurement data for bubble growth and applied to bubble collapse and rebound. By a comparison with Navier-Stokes results from literature, the homobaricity assumption is shown to be appropriate even in the last stage of bubble collapse. The relation of the local velocity and temperature field with heat and mass transfer is discussed. Equilibrium bubble interface conditions (liquid and gaseous side have the same temperature and chemical potential) are compared to non-equilibrium conditions and are shown to yield the same local velocity and temperature field for each stage of bubble collapse and rebound. [ABSTRACT FROM AUTHOR]

• The economic performance of a maintenance policy with imperfect inspections is analyzed; • A new CBM policy with a two-stage inspection scheme is proposed by mixing both perfect and imperfect inspections; • Numerical experiments and a real case study show the advantages of the proposed policies; • By studying the effect of inspection quality mis-specification, the proposed two policies are found to be more robust. A condition-based maintenance (CBM) strategy is now recognized as an efficient approach to perform maintenance at the best time before failures so as to save lifetime cycle cost. For continuous degradation processes, a significant source of variability lies in measurement errors caused by imperfect inspections, and this may lead to "false positive" or "false negative" observations, and consequently to inopportune maintenance decisions. To the best of our knowledge, researches on CBM optimization with imperfect inspections remain limited for continuous degradation processes, even though the subject is of practical interest for the implementation of a CBM policy. Imperfect inspections are indeed imperfect but still return interesting information on the system degradation level, and making them perfect can be expensive. Therefore, we analyze the economic performance of a maintenance policy with imperfect inspections, and compare it with the classical policy with perfect inspections to see which policy offers the best benefit in a given situation. Furthermore, a CBM policy with a two-stage inspection scheme is proposed to take benefit of mixing both perfect and imperfect inspections in the same maintenance policy. Through numerical experiments and a real case study, it is shown that the policy with imperfect inspections can be better than the classical one, and that the proposed policy with a two-stage inspection scheme always leads to the minimum long run maintenance cost rate. [ABSTRACT FROM AUTHOR]

• Inconsistencies in the MUSIG population balance model are identified. • A new discrete formulation for population balance equation is presented. • The updated MUSIG model preserves both mass and number of bubbles. • The necessity of the updates is demonstrated by analytical and experimental data. • A reliable framework for validating coalescence & breakup models is proposed. The MUSIG (Multiple Size Group) model in the commercial CFD code ANSYS CFX is a population balance approach for describing binary bubble coalescence and breakup events. It is widely used in the simulation of poly-dispersed bubbly flows. The purpose of this work is to identify the internal inconsistencies in the discrete method that is applied for the solution of the population balance equation in MUSIG, and to propose an internally consistent one for discretising the source and sink terms that result from bubble coalescence and breakup. The new formulation is superior to the existing ones in preserving both mass and number density of bubbles, allowing arbitrary discretisation schemes and is free of costly numerical integrations. The numerical results on the evolution of bubble size distributions in bubbly flows reveal that the inconsistency in the original MUSIG regarding bubble breakup is non-negligible for both academic and practical cases. The discussion on the effect of internal inconsistency as well as updates to the model presented in this work are necessary and important for calibration of bubble coalescence and breakup models using the MUSIG approach. [ABSTRACT FROM AUTHOR]

• A Volume of Fluid based approach to model growth of a pre-existing bubble in a supersaturated solution is presented. • Transport of the dissolved gas is modelled using Compressive Continuous Species Transfer model. • A continuum-field representation, previously developed for evaporation, of source terms is implemented. • The bubble growth predicted using Sherwood number based correlation and Ficks 1st law are compared. • The effect bubble growth on its rise velocity is also investigated. In this paper, a Volume of Fluid (VOF) based approach to simulate the growth of a pre-existing bubble in a supersaturated solution is developed and implemented in OpenFOAMⓇ. The model incorporates the Compressive Continuous Species Transfer approach to describe the transport of dissolved gas and surface tension is treated using the Sharp Surface Force method. The driving force for bubble growth is defined using Fick's 1st law and a Sherwood number based correlation. The source terms for the governing equations are implemented by extending the work by Hardt and Wondra, J. Comp. Phys. 227 (2008) 5871–5895. The predictions of the proposed solver is compared against theoretical models for bubble growth in supersaturated solutions. The effect of spurious currents, which are generated while modelling surface tension, on bubble growth is also investigated. The proposed approach is used to model the growth of a rising bubble in the supersaturated solution. [ABSTRACT FROM AUTHOR]

• A two-stage degradation system with two performance characterizes is considered. • A correlated bivariate Wiener process is adopted in modeling. • The explicit expressions of system reliabilities and availabilities are derived. • Two algorithms for the simulations of system reliabilities are given. It is still a challenge to study the degradation mechanisms of complex systems with multiple performance characteristics. This paper develops a two-stage stochastic degradation model. The degeneration processes of two correlated performance characteristics are described by a correlated bivariate Wiener process in the first stage, in which neither of the degradation levels of performance characteristics reaches their thresholds. When one of the degradation levels of performance characteristics reaches its threshold, the system operates defectively in the second stage, and the system degradation process is described by the other performance characteristic which is modeled by a univariate Wiener process. The system fails completely when both the degradation levels of performance characteristics reach their thresholds. Explicit expressions of the system reliability and availabilities are given based on different inspection and maintenance policies. Simulation is also presented, and it shows that the analytical results and the simulation results are in good agreement. Finally, a detailed case study of the rail track geometry degradation is given to demonstrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

• Improved numerical results with higher grid resolution. • New study on the impact of contact angle during bubble formation. • Different periodicity observed with fixed gas flow rate. • Simulation and comparison of inserted tubes. Bubble formation from a submerged orifice is widely applied in bio-process and chemical reaction systems. In this study, the effects of different orifice diameters and contact angles in Period-I and Period-II regimes are studied systematically on a 2D axisymmetric domain. Simulation results are presented from the formation of the first bubble and explained by means of the surrounding fluid field, bubble interaction, and bubble aspect ratio. The orifice diameter is varied from 0.6 mm to 3 mm. The numerical results show that the detachment time of all bubbles remains constant (in time) for smaller orifice diameters (d a ≤ 1.5 mm), while the detachment time of the first bubble is different from the rest of the bubbles for larger orifice diameters (d a ≥ 2 mm), which is due to the different surrounding flow field. Contact angles from 60° to 165° are considered for the gas flow rates in the regime of bubble pairing, and it is observed that the bubble detachment time decreases when the contact angle increases, and it converges to a constant value when the contact angle is larger than 135°. In addition, the transition from period doubling to deterministic chaos (in which there is a variable number of bubbles within each period) is observed. A new scenario of inserting a submerged tube upward into the liquid is considered and compared to the previous cases. It is observed that when the tube is vertically inserted into the liquid, the bubble detachment time is even smaller because of higher influence from the surrounding liquid field, leading to a different phenomenon from the non-inserted tube cases. [ABSTRACT FROM AUTHOR]

• A new Weibull inter-arrival shock process is proposed to model the competing risk process. • The closed forms of reliability function are derived in three shock failure models. • Optimal renewal age is derived numerically by minimizing the long run system cost. In this paper, a new Weibull inter-arrival shock process is proposed for modeling the competing risk process. The dependent competing failure/risk processes exists in many systems and the reliability modeling for those processes has attracted much attention in the recent years. However, the arrivals of random shocks are usually modeled as Poisson process which indicates the constant hazard rate of shock inter-arrival time. Our proposed Weibull inter-arrival shock process generalized the Poisson shock process and can deal with the cases when the shock count data are over-dispersion or under-dispersion. On the other hand, the dependency between the soft failure process and hard failure process is emphasized by assuming the linear dependent damage size. In four different hard failure models, analytic forms of the reliability functions are derived by using the polynomial expansion. The maintenance optimization for the developed model is discussed under different shock failure mechanisms. Numerical examples based on a micro-engine are also presented to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

• A novel failure interaction framework is constructed considering hazard rate increment. • Environmental uncertainties are incorporated into dependent failure processes. • A new group maintenance strategy is developed to prevent dependent failures. • The applicability is validated by a case study on an electrical distribution system. Failure dependence is a common phenomenon in complex and large-scale industrial plants, which may cause tremendous economic losses and unacceptable safety risks. This paper investigates an advanced group and opportunistic maintenance policy for a two-component system with failure interaction. The interaction between soft and hard failures is characterized by random hazard rate increments, with fully consideration of environmental uncertainties. To sufficiently utilize the economic dependence between components, Scheduled maintenance windows are equally spaced for group maintenance of the whole system. Whenever a component is replaced at a maintenance window, the other one is also opportunistically replaced. Furthermore, failure of component 2 is removed by minimal repair, whereas replacement is left to the subsequent window. The objective is to jointly optimize the maintenance interval and the number of maintenance windows via the artificial bee colony algorithm. A case study on an electrical distribution system is provided to validate the applicability of the adopted policy. [ABSTRACT FROM AUTHOR]

• The mathematical model on the excited vibration is developed based on the parabola curve of the bubble profile. • The incremental harmonic balance method is used to solve the equation and an experiment is performed. • The amplitude–frequency curve and phase-curve for the vibration system are given. In the present study, we investigate the nonlinear forced vibration of a bubble-mass system both theoretically and experimentally, where the bubble is viewed as a spring. The mathematical model on the excited vibration is developed by assuming the contour line of the bubble being a parabola curve. The incremental harmonic balance method is used to solve the ordinary differential equation, and the high speed video camera is utilized to take photographs. The effects of the bubble volume and radius of the plate on the static compression of the spring, the amplitude–frequency curves for the fundamental and second harmonic wave, and phase–frequency curve of the fundamental wave, are all demonstrated. The results show that the spring representing the bubble is always in compression in the process of vibration, and a greater bubble volume and a smaller plate radius make the system stiffness smaller. The second harmonic wave has some different characteristics from the counterparts of the fundamental wave. We also perform an experiment to validate these theoretical analyses. This study sheds new light on the nonlinear vibration of soft system, which may be beneficial to such areas as aerospace, microgravity, and soft robotics. [ABSTRACT FROM AUTHOR]

Modified complex potential with free traction boundary condition is used to formulate the curved crack problem in a half plane elasticity into a singular integral equation. The singular integral equation is solved numerically for the unknown distribution dislocation function. Numerical examples exhibit the stress intensity factor increases as the cracks getting close to each other, and close to the boundary of the half plane. [ABSTRACT FROM AUTHOR]

This study deals with the use of Generalized Finite Difference Method (GFDM) in Perfectly Matched Layer (PML) analysis. There are two options for performing PML analysis. First option is to express PML equations in terms of real coordinates of the points in actual (real) PML region; the second is to use governing equations (expressed in terms of complex stretching coordinates) as they are in complex PML region. The first option is implemented in this study; the implementation of the second option is under way and will be reported in another study. For the integration of PML equations, the use of GFDM is proposed. Finally, the suggested procedure is assessed computationally by considering the compliance functions of surface and embedded rigid strip foundations. GFDM with PML results are compared to those obtained by using Finite Element Method (FEM) with PML and Boundary Element Method (BEM). Excellent matches in results showed the reliability of the proposed procedure in PML analysis. [ABSTRACT FROM AUTHOR]

In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also exhibit chaotic behaviour in the phase space. In this paper, we extend our previous finding to explore yet another gallery of new chaotic attractors which are derived from the original Lorenz system of equations. Compared to the previous exploration with sinusoidal type transcendental nonlinearity, here we focus on only cross-product and higher-power type nonlinearities in the three state equations. We here report over 150 different structures of chaotic attractors along with their one set of parameter values, phase space dynamics and the Largest Lyapunov Exponents (LLE). The expressions of these new Lorenz-like nonlinear dynamical systems have been automatically evolved through multi-gene genetic programming (MGGP). In the past two decades, there have been many claims of designing new chaotic attractors as an incremental extension of the Lorenz family. We provide here a large family of chaotic systems whose structure closely resemble the original Lorenz system but with drastically different phase space dynamics. This advances the state of the art knowledge of discovering new chaotic systems which can find application in many real-world problems. This work may also find its archival value in future in the domain of new chaotic system discovery. [ABSTRACT FROM AUTHOR]

In this article, an analytical solution is presented for coupled thermoelasticity analysis (with energy dissipation) in a micro/nano beam resonator, considering small scale effects on the transient behaviors of fields’ variables. The Green–Naghdi (GN) theory of generalized coupled thermoelasticity and nonlocal Rayleigh beam theory (NRBT) are employed to derive the temperature and lateral deflection in the closed forms. The presented analytical solution is based on Laplace transform. To find the dynamic and transient behaviors of fields’ variables in time domain, an inversion Laplace technique is utilized, which is called Talbot method. The effects of some parameters such as small scale parameter and dimensions of the beam on the dynamic behaviors of temperature and lateral deflections are discussed in details. The propagation of wave fronts in both temperature and lateral deflection domains are obtained and graphically illustrated at various time instants. [ABSTRACT FROM AUTHOR]

This paper presents a method for determining the nonlinear dynamic responses of structures under moving loads. The load is considered as a four degrees-of-freedom system with linear suspensions and tires flexibility, and the structure is modeled as an Euler–Bernoulli beam with simply supported at both ends. The nonlinear dynamic interaction of the load–structure system is discussed, and Kelvin−Voigt material model is employed for the beam. The nonlinear partial differential equations of the dynamic interaction are derived by using the von Kármán nonlinear theory and D'Alembert's principle. Based on the Galerkin method, the partial differential equations of the system are transformed into nonlinear ordinary equations, which can be solved by using the Newmark method and Newton−Raphson iteration method. To validate the approach proposed in this paper, the comparison are performed using a moving mass and a moving oscillator as the excitation sources, and the investigations demonstrate good reliability. [ABSTRACT FROM AUTHOR]

Mathematical model of a wind-powered vehicle is proposed. The vehicle uses a wing to convert the energy of an upcoming wind flow into the energy of the mechanical motion in such a way that the vehicle goes against the wind. The corresponding dynamical system is constructed. Parametric analysis of the system is carried out using the Poincare-Pontryagin asymptotic approach. The existence of an attracting steady regime is shown. Boundaries of applicability of asymptotic estimations are analyzed using numerical simulation. Results of the parametric analysis were used for construction of a prototype of such a vehicle. Experiments with this prototype qualitatively agree with the mathematical modeling. [ABSTRACT FROM AUTHOR]

Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type line search equipped with some popular nonmonotone terms. More specifically, we propose two novel nonmonotone terms, combine them into Armijo’s rule and establish the global convergence of sequences generated by these schemes. Furthermore, we report extensive numerical results and comparisons indicating the performance of the nonmonotone Armijo-type line searches using the most popular search directions on the CUTEst test collection of unconstrained problems. We finally apply the considered nonmonotone schemes to a deblurring problem to recover a blurred/noisy image. [ABSTRACT FROM AUTHOR]

Recently, Zhou et al. proposed the C-IVIFOWA operator for aggregating interval-valued intuitionistic fuzzy numbers. The flaws of the C-IVIFOWA operator are illustrated by two counter-examples. The aim of this short communication is to show how the existing aggregation operator can be improved to increase accuracy. Some desirable properties of the revised C-IVIFOWA operator are studied in detail. [ABSTRACT FROM AUTHOR]

The present paper provides a systematic treatment of various decomposition methods for linear (and some model nonlinear) systems of coupled three-dimensional partial differential equations of a fairly general form. Special cases of the systems considered are commonly used in applied mathematics, continuum mechanics, and physics. The methods in question are based on the decomposition (splitting) of a system of equations into a few simpler subsystems or independent equations. We show that in the absence of mass forces the solution of the system of four three-dimensional stationary and nonstationary equations considered can be expressed via solutions of three independent equations (two of which having a similar form) in a number of ways. The notion of decomposition order is introduced. Various decomposition methods of the first, second, and higher orders are described. To illustrate the capabilities of the methods, more than fifteen distinct systems of coupled 3D equations are discussed which describe viscoelastic incompressible fluids, compressible barotropic fluids, thermoelasticity, thermoviscoelasticity, electromagnetic fields, etc. The results obtained may be useful when constructing exact and numerical solutions of linear problems in continuum mechanics and physics as well as when testing numerical and approximate methods for linear and some nonlinear problems. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic response of homogeneous, transversely isotropic, thermoelastic micro-beam resonators subjected to time-varying transverse loads has been investigated in the context of generalised theory of thermoelasticity. The micro-beam is modeled based on Euler–Bernoulli beam theory. The beam is assumed to be at clamped–clamped conditions at its axial ends. The analytical solution has been obtained by using the Laplace transform technique in the time domain. The inversion of the transformed solution has been carried out by using calculus of residues. The analytical expressions for deflection obtained in the physical domain have been computed numerically for a silicon micro-beam with the help of MATLAB software. The numerically analysed results for deflection of clamped–clamped thermoelastic silicon (Si) micro-beam with length, time and frequency ratio due to acting dynamic loads have been presented graphically. The present model may be used in microelectromechanical applications such as relay switches, frequency filters, mass flow sensors, accelerometers and resonators. [ABSTRACT FROM AUTHOR]

Elastomer seals are growing in popularity in various applications in the oil and gas sector, and in many other fields. In this paper, the deformation of an elastomer seal confined between a metal tube and a rigid casing is analytically investigated. The elastomer is strained radially against the casing by means of a controlled tubular expansion process. The elastomer is also naturally strained axially by means of annuls reservoir fluid. The total strain causes the elastomer to develop internal pressure which leads to the sealing effect. The developed analytical results show the effect of elastomer geometry and its material properties on sealing performance in terms of maximum sealing pressure. In addition, sealing performance of the elastomer is studied under different strain conditions. The main contribution of this work is in finding a closed-form solution for the sealing pressure distribution along the axial direction of the elastomer as a function of compression ratio, seal geometry, and material properties. This analytical model can be used by field engineers for selection and evaluation of elastomer materials for a given set of field conditions, and by developers for improvement of elastomer seal design. [ABSTRACT FROM AUTHOR]

Differential equations are widely used to model physical phenomena in the real world. In the present work, a nontraditional modified ant colony programming (ACP) method is implemented. The modified ACP algorithm is unique as it does not use the criteria of distance. It utilizes the probability function which related to the quantity of the pheromone level in the ACP. The motivation in this present work is to describe the consistency and the applicability of the nontraditional ant colony programming (ACP) method in solving various ordinary differential equations (ODE’s) and partial differential equations (PDE’s) problems. Comparatively, similar and exact solution is achieved by using the ACP approach. Illustrative numerical example as well as tables are presented for comparison purpose. [ABSTRACT FROM AUTHOR]

In this study, we propose a new scheduling model with position-dependent deterioration, in which the processing time of a job is defined by an increasing function of total weighted normal processing time of jobs prior to it in the sequence, where the weight is position dependent. We show that some single machine scheduling problems remain polynomially solvable under the proposed model, respectively. In addition, we show that some special cases of the flow shop scheduling problems can be optimally solved by polynomial time algorithm, respectively. [ABSTRACT FROM AUTHOR]

This paper begins by discussing an improved interpolating moving least-square (IIMLS) method and the properties of its shape function. In the IIMLS method, the shape function is of delta function property and the weight function is nonsingular, so it overcomes the drawbacks in both the moving least-square approximation and the interpolating moving least-square method. Then combining boundary integral equations with the IIMLS method, an interpolating boundary element-free method (IBEFM) is developed for three-dimensional potential problems. In the IBEFM, only a nodal data structure on the boundary face of a domain is required. Unlike the boundary node method (BNM), the IBEFM is a direct meshless method in which the primary unknown quantities are real solutions of nodal variables, and boundary conditions can be imposed directly and easily, which leads to a greater computational precision. Besides, the number of both unknowns and system equations in the IBEFM is only half of that in the BNM, and thus the computing speed and efficiency are increased. Numerical examples on curve/surface fittings and potential problems indicate that the efficiency and convergence rate of the present methods is high. [ABSTRACT FROM AUTHOR]

In this paper the construction and dynamic modeling of a mobile ball robot is represented. The unique mechanical structure of this robot results more reliable and stable motion with respect to previous similar robots. Driving mechanism is placed within a hollow spherical case, and consists of three sets of actuated omni–wheels for omni-directional motion of the robot. This mechanism decreases relative slip between the inner actuation system and outer ball case, and results more precise control of the robot in different paths and places. At first, the mechanical structure, actuation and control system, and process of different components assembling to work as a robot is explained. Then, based on the Newton–Euler formulation, mathematical model of motion is derived and dynamic equations of the robot are evaluated. These equations have differential algebraic equations (DAEs) formation. Consequently, a computational method to solve ADEs has been developed. Finally, in a case study, the robot performance in passing through a linear path with two perpendicular segments is studied. Simulation and experimental results demonstrate that robot moves through the desired and predefined trajectory. [ABSTRACT FROM AUTHOR]

In this paper, the problem of delay-dependent exponential stability criteria for neutral-delay system with nonlinear uncertainties is considered. By constructing a new class of Lyapunov–Krasovskii functionals and using the free-weighting matrices methods within a convex optimization approach, some less conservative delay-dependent stability criteria of neutral delay differential system with nonlinear uncertainties is obtained. These stability conditions are solved as linear matrix inequalities which can be easily solved by various convex optimization algorithms. Finally, numerical examples are given to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

A new computational intelligence technique is presented for solution of non-linear quadratic Riccati differential equations of fractional order based on artificial neural networks (ANNs) and sequential quadratic programming (SQP). The power of feed forward ANNs in an unsupervised manner is exploited for mathematical modeling of the equation; training of weights is carried out with an efficient constrained optimization technique based on the SQP algorithm. The proposed scheme is evaluated on two initial value problems of the Riccati fractional order equation with integer and non-integer derivatives. Comparison of results with the exact solution, and with reference numerical methods demonstrates the correctness of the proposed methodology. Performance of the proposed scheme is also validated using results of statistical analysis based on a sufficiently large number of independent runs. [ABSTRACT FROM AUTHOR]

Based on the concept of uncertain process, an uncertain optimal control model is established for switched systems. A two-stage algorithm is introduced to handle such model. In the first stage, the minimum value of the cost function and the bang–bang control are obtained under fixed switching instants, and in the second stage, the modified golden section method is used to solve an optimization problem. An example is shown to validate the method. [ABSTRACT FROM AUTHOR]

Using an iterative method based on the Sumudu transform, we have solved a system of non-linear partial differential equations, which is derived from attractor for Keller–Segel dynamics system. Graphical representations are provided and display biologically reasonable dependencies of the parameters values. The reliability of the SHPM and the reduced number of computations make the method broadly applicable. In addition, the SHPM calculations are very simple and straightforward. This study demonstrates that SHPM is a powerful and efficient tool for solving non-linear partial differential equations. [ABSTRACT FROM AUTHOR]

A system of m coupled van der Pol oscillators is considered. The dynamical behavior around 1 : γ ( γ ∈ R + , γ ≠ 1 , 2 , 3 ) double Hopf bifurcation point is studied analytically. By using the method of multiple scales, the amplitude equations are obtained. Two parameters including time delay and the coupling strength are chosen as the bifurcation parameters, and then the dynamical behavior arising from the bifurcation is classified qualitatively in two-parameter plane. Some interesting dynamical phenomena including amplitude death, periodic solution and coexisting periodic solutions are obtained. By fixing m or γ , the effects of the changes of γ or m on the dynamics are investigated, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient numerical method in the context of variational formulation and on the basis of Rayleigh–Ritz technique to address the free vibration problem of laminated composite conical shells. To this end, the energy functional of Hamilton’s principle is written in a quadratic form using matrix relations first. Displacements are then approximated via a linear combination of base functions, by which the number of final unknowns reduces. After that, the strain tensor is discretized by means of matrix differential quadrature (DQ) operators. In the next step, using Taylor series and DQ rules, a matrix integral operator is constructed which is embedded into the stiffness matrix so as to discretize the quadratic representation of energy functional. Finally, the reduced form of mass and stiffness matrices are readily obtained from the aforementioned discretized functional. To obtain the natural frequencies of conical shell, hybrid harmonic-beam base functions are employed as modal displacement functions. The accuracy of the present numerical method is examined by comparing its results with those from the published literature. It is revealed that the method is capable of accurately solving the problem with a little computational effort and ease of implementation. [ABSTRACT FROM AUTHOR]

The detection of defects due to corrosion in oil pipeline industry is very important. Detecting corrosion by electrical field can be modeled as a Cauchy problem for a Laplace equation in an annulus domain, which is well known to be severely ill-posed. In this paper, a modified Tikhonov regularization method is proposed. And a Hölder-type error estimate is achieved, which is order optimal according to the general regularization theory. Moreover, a Fast Fourier Transform (FFT) is used in the numerical implementation. Finally, numerical results show that the regularization method and FFT work well. [ABSTRACT FROM AUTHOR]

The application of sustainability principles into supply chains is an evolving research area currently suffering from a scarcity of established theories, models, and frameworks. There are at least two key reasons why it is difficult to build sustainability into the supply chain. First, there are numerous context dependent factors that either enable or hinder progress towards sustainability in a supply chain. There is a need to better understand how these factors affect the sustainability performance of supply chains. Second, implementing sustainability requires a triple bottom line approach, where improvements are pursued in the environmental, economic, and social dimensions of performance. These two challenges mean that implementing sustainability in a supply chain is a complex process that involves a large number of interacting factors. This paper contributes to efforts to overcome these challenges by proposing a mathematical model for assessing sustainability in the supply chain. The model is based on the notion that a probabilistic representation of sustainability can realistically account for its challenges. The development of the proposed model was guided by the need for ease of use, simplicity, and the ability to quickly provide feedback on the sustainability status of supply chains over time. [ABSTRACT FROM AUTHOR]

The large deflection of an elastic cantilever rod pulled by cable is analyzing in terms of the Jacobi elliptical functions. The problem is reduced to solution of a system of two transcendental equations which allow defining six different problems. All these problems are discussions and illustrated with graphs of equilibrium shapes and tables providing some reference numerical values. [ABSTRACT FROM AUTHOR]

In this paper, an approach for approximating the fuzzy linear system of differential equations under generalized differentiability is presented, because under this interpretation, we may obtain solutions which have a decreasing length of their support. In several applications the behavior of these solutions better reflects the behavior of some real-world systems. Also, we investigate a necessary and sufficient conditions for the solution vector to be a fuzzy vector. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis of the one-dimensional Klein–Gordon equation with quadratic and cubic nonlinearity, using the element-free reproducing kernel particle Ritz method (kp-Ritz method). Approximation of the wave displacement is expressed according to a set of meshfree kernel particle functions. Based on the established functional corresponding to the nonlinear Klein–Gordon equation, a system of nonlinear discrete equations can be obtained by applying the Ritz minimization procedure. The Newmark integration scheme combined with an iterative technique is applied to the resulting nonlinear system equations. Numerical examples are tested to validate the proposition that the presented numerical solutions are in good agreement with analytical results available in extant literature. [ABSTRACT FROM AUTHOR]

The Moving Particle Semi-implicit method (MPS) shows great potential to simulate violent incompressible free surface flows. However, Direct Numerical Simulations of such turbulent flows by particle methods would be extremely time-consuming. Taken ideas from the Sub-Grid Scale (SGS) model in grid-based Large Eddy Simulation (LES), static and dynamic Smagorinsky models are specially designed for Sub-Particle Scale (SPS) model in MPS. These SPS models are discretized by the combination of gradient and divergence models in MPS and the semi-implicit algorithm to implement MPS-LES is developed. The widely-studied mixing layer flows are simulated to quantitatively validate the developed turbulence particle model. Both the turbulent statistical profiles and vortex pairing processes are in good agreements with experimental observations after the SPS model is adopted. Moreover, it is found that the performance of the dynamic Smagorinsky model is better than that of the static model. [ABSTRACT FROM AUTHOR]

A combination method of finite element method and accelerated two-grid scheme is constructed for solving numerically the two-dimensional Steklov eigenvalue problem. This algorithm involves solving a small Steklov eigenvalue problem on the coarse mesh with mesh size H and a linear algebraic system on the fine mesh with mesh size h . By solving a slightly different linear problem on the fine grid, the computation will be more effective and convenient and the scaling between H and h becomes h = O ( H 4 ) , which can save a large amount of computational time. Finally, numerical tests confirm the theoretical results of the presented method. [ABSTRACT FROM AUTHOR]

The axisymmetric vibration of three kinds of zigzag, armchair and chiral single-walled carbon nanotubes (SWCNTs) in water is studied in the paper based on the nonlocal anisotropic shell model. The present model is justified compared with the existing experimental observation and available data in literature. It is shown that for the tubes with the same diameter, the radial breathing frequencies from lower to upper limits are zigzag, chiral and armchair tubes, respectively. However, the difference in frequency diminishes with the increase of diameter. Furthermore, we found that the axisymmetric radial, longitudinal and torsional vibrational frequencies of SWCNTs are mainly sensitive to the values of radius and the scale coefficient, but cannot be substantially changed by their atomic structure. Moreover, we can get that the local shell model for CNT analysis would lead to an overprediction of the vibrational frequencies of almost all modes. So the nonlocal isotropic continuum models are practical in analyzing CNTs of large geometric sizes. Finally, the results show that the effects of fluid motion surrounding CNTs can be ignored for the large wave numbers. [ABSTRACT FROM AUTHOR]

The modified couple stress theory, as a theory capable of capturing size effects, is implemented to study the vibration characteristic of a postbuckled microbeam. To this end, a modified couple stress Euler–Bernoulli beam model containing geometric nonlinearity is considered. Within the framework of a variational formulation and based on Hamilton’s principle, the governing equation and corresponding boundary conditions are derived. By eliminating time-dependent terms, the governing equation of vibration is reduced to that of buckling problem for the microbeam subjected to an axial load. The critical buckling loads and their corresponding mode shapes are predicted through an exact solution for various boundary conditions. Afterwards, the vibration analysis of a simply-supported microbeam is investigated around the obtained postbuckling configuration. It is found that the stiffness of microbeam predicted by the modified couple stress model is higher than that predicted by the classical model. Additionally, it is demonstrated that the natural frequencies by considering all of the vibration modes except the first mode are independent of the buckling load. The influences of the dimensionless length-scale parameter, Poisson’s ratio, various boundary conditions and the number of buckled modes on the critical buckling loads and natural frequency are fully investigated. [ABSTRACT FROM AUTHOR]

An extension of the integrated production–delivery lot sizing model under stochastic delivery time with transportation cost is investigated. The delivery time is assumed to be exponentially distributed. The presumption, the optimum delivery quantity determining the minimum of the transportation cost, has been widely adopted in transportation management models. Hence, we model the transportation cost as a function of delivery quantity. We consider comprehensive costs in the optimization problem. The expected total cost per unit of time with respect to the delivery quantity is proved to be a convex function under certain feasible conditions. As a result of computational studies, our proposed production–delivery decision model has shown notably adaptable when the delivery time is random. In particular, when the producer’s and retailer’s carrying costs are low, and/or mean time of delivery and transportation costs are high, our suggested policy saves more than 9% as opposed to the scheme recommended by prior researches, which manifests highly advanced gains. [ABSTRACT FROM AUTHOR]

This study focuses on the nonlinear dynamic characteristics of a single-machine infinite-bus (SMIB) power system under a periodic load disturbance. The qualitative behavior of this system is described by the well-known “swing equation”, which is a nonlinear second-order differential equation. Compared with the existing results, the generator damping in this paper, which is more close to the practical engineering, is related to the state variables of this system. In addition, Melnikov’s method is applied to obtain the threshold for the onset of chaos. The efficiency of the criteria for chaotic motion is verified via numerical simulations. Comparisons between the theoretical analysis and numerical simulation show good agreements. The results in this paper will contribute a better understanding of the nonlinear dynamic behaviors of the SMIB power system. [ABSTRACT FROM AUTHOR]

A semi-analytical procedure is presented to study the dynamic cross-interference among a group of long strip foundations on an elastic half-space, which is simplified as a two-dimensional problem. In addition to analytical solutions in terms of Green functions, a discretization method is applied to determine the lateral/rocking dynamic impedances of a foundation group. To determine the unknown contact stresses between the foundations and the supporting medium, the soil-foundation interfaces are discretized into a series of strip elements which are only subjected to constant lateral and vertical tractions. Multiple foundations with different widths and separation distances are considered in the formulations. For the time history analysis of those strongly frequency-dependent impedances of a foundation group through a substructure approach, complex Chebyshev polynomials are used to fit the lumped-parameter (L-P) model in the domain-transformation. Numerical results over a wide range of vibration frequencies for impedance calculation are verified with the existing methods. The effects of cross-interference on contact stress distributions and impedances for a group of two and three rigid foundations are discussed in detail. Finally, the accuracy and the validity of the L-P model are rigorously studied by simulating adjacent foundations on an elastic half-space within a close distance. [ABSTRACT FROM AUTHOR]

In this paper, we use quadratic B-splines to reconstruct an approximating function by using the integral values of successive subintervals, rather than the usual function values at the knots. It is called integro quadratic spline interpolation. Compared to the other existing methods, our method can tackle integro interpolation problem from the integral values on arbitrary successive subintervals. The general approximation error is studied and the super convergence property is also derived when the interval is equally partitioned. Moreover, it can work successfully without any boundary condition. Numerical experiments show our method is easy to implement and effective. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce both the concept of fuzzy extension of a classical function for modelling imprecise relations between variables and the basic arithmetic operations which this entails. The concept of fuzzy extension can be considered as a generalisation of the concept of classical function extended to the field of the fuzzy sets defined in R . The fuzzy extension f ‾ of a classical continuous function f ( x ) is a particular kind of fuzzy relation, which describes the correspondence between two variables x and y . The univocal image of each value of x through f ‾ is a closed interval of y values [ f l ( x ) , f u ( x ) ] . Functions f l ( x ) and f u ( x ) set the limits of the y interval whose extent of correspondence to x is nonzero, being zero ∀ y : y ⩽ f l ( x ) and ∀ y : y ⩾ f u ( x ) and they fulfill the condition that ∀ x ∈ Df l ( x ) ⩽ f ( x ) ⩽ f u ( x ) . A fuzzy extension f ‾ is defined by its membership function μ f ‾ ( x , y ) , which quantifies the extent to which each value of the y variable corresponds to each value of x . The image y ‾ of each fuzzy set x ‾ is achieved by means of the composition rule of f ‾ . In order to perform arithmetic operations with fuzzy extensions, the following basic operations are defined: the addition a ‾ , subtraction s ‾ , multiplication m ‾ and division d ‾ of two fuzzy extensions. The concept of fuzzy extension of a classical function, the procedure to specify and model μ f ‾ ( x , y ) , the procedure to determine the image y ‾ and the arithmetic operations are graphically illustrated and properly exemplified. A fuzzy extension f ‾ defined in this way is a useful alternative to the set of fuzzy rules or knowledge base for modelling inherently imprecise relations, which are frequently described in a simplified manner by means of classical functions. For this reason, fuzzy extensions can be applied to a number of different fields, being particularly suitable for environmental assessments, such as the design and evaluation of environmental quality indexes and the environmental impact assessments, among others. [ABSTRACT FROM AUTHOR]

The iterative learning control problem of strict feedback nonlinear system with unknown time-varying parameters and uncertain control direction is an open problem. An iterative learning control strategy is presented for a class of nonlinear time-varying systems with unknown control direction to solve the non-uniform trajectory tracking problem. Backstepping design technique is applied to deal with system dynamics with non-global Lipschitz nonlinearities. Based on the Lyapunov-like synthesis, we show that all signals in the closed-loop system remain bounded over a pre-specified time interval [ 0 , T ] , and complete non-uniform trajectory tracking of the system output is achieved. The time-varying parameters are expanded into Fourier series with bounded remained term. A typical series is introduced in order to deal with the unknown bound of remained term and the non-uniform trajectory tracking. Nussbaum function is used to deal with unknown control direction. Finally, a simulation example shows the feasibility and effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this study, we develop multi-item multi-objective manufacturer–retailer supply chain models with risk and budget constraints for long-term contracts with a profit sharing scheme in a fuzzy-stochastic environment. The manufacturing costs of the items are fuzzy and the demands for the items are random during each period. We examine two separate models with crisp and probabilistic budget constraints for long-term contracts where the business relationship is repeated, while demand is uncertain in a stochastic sense. The models are formulated as profit maximization problems. Next, the fuzzy compromise programming method, global criteria method, and weighted sum method are used to reduce the multi-objective problems into their corresponding single objective problems. Finally, the problems are solved using a gradient-based nonlinear programming technique: the generalized reduced gradient method. The models are illustrated with numerical examples for different types of stochastic demand and a comparative study is presented. [ABSTRACT FROM AUTHOR]

A new approach for modeling the equations that govern the motion of a projectile in a uniform gravitational field is presented. In this study, the fractional derivatives and quadratic-drag term are introduced to make the model more realistic. The formulated mathematical model is non-linear coupled fractional-order system where fractional derivatives are in Caputo sense. These equations are analytically solved by using the recently modified fractional differential transform method. The results obtained from a numerical case study are compared to those of the corresponding integer-order model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the proposed method. [Copyright &y& Elsevier]

Abstract: We study a single-machine scheduling and due window assignment problem, in which job processing times are defined by functions of their starting times (deteriorating effect) and positions in the sequence (learning effect). The problem is to determine the optimal due windows and the processing sequence simultaneously to minimize costs for earliness, tardiness, the window location, window size and makespan. We show that the problem remains polynomially solvable under the proposed model for two popular due window assignment methods: The slack due date assignment method (usually referred to as SLK) and the unrestricted due date assignment method (usually referred to as DIF). [Copyright &y& Elsevier]