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Physics-informed neural networks (PINN) architectures have been recently explored to accelerate hemodynamics simulations by leveraging mathematical models for blood flow and empirical data. In this paper, a variable separated physics-informed neural networks based on adaptive weighted loss functions (AW-vsPINN) is developed for blood flow model in arteries. In particular, sub-neural networks are proposed to separately predict the unknown scalar state variables by sharing the same input layer. The AW-vsPINN adaptively adjusts the weights of loss terms by the minmax algorithm, which will be updated synchronously along with the network parameters and can balance the contributions of different loss terms during training. The two-stage optimization is implemented to train the neural networks. Specifically, the Adam optimizer is iterated for initial steps with the learning rate generated by the inverse time decay scheduler, and then the L-BFGS optimizer continues to train until the loss converges. Numerical results illustrate that the AW-vsPINN can remarkably improve prediction accuracy and enhance the ability of generalization compared to the conventional PINN. The proposed AW-vsPINN framework has high potential in predicting the blood flow information in cardiovascular disease. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple and fast shape transformation method. This method is based on the Allen-Cahn (AC) partial differential equation and uses the edge stop function to constrain evolution. We use the operator splitting method to control the equation for splitting, and use the explicit Euler's method to solve the discrete equation. Based on the source shape and the target shape, our phase-field model can perform rapid shape transformation when the appropriate parameters are selected. In order to verify the feasibility of our proposed phase-field model, numerical experiments on shape transformation are carried out in two-dimensional and three-dimensional space. The results show that the established mathematical model can not only perform shape transformation between simple shapes, but also have a good effect on shape transformation between complex shapes. We also propose a numerical solution using the Crank-Nicolson numerical scheme to handle the model we introduced. This numerical scheme utilizes the multigrid method and Gauss-Seidel iteration for solving. The results of the numerical experiments demonstrate the effectiveness of this numerical method in handling shape transformations in three-dimensional space. [ABSTRACT FROM AUTHOR]

Ultrasound enhanced drug transport is a multiphysics problem involving acoustic waves propagation, bioheat transfer, and drug transport. In this paper, we study a model for this problem that consists of a wave-type equation for acoustic pressure, a diffusion-reaction equation for bioheat transfer, and a convection-diffusion-reaction equation for drug transport. We focus in particular on the numerical analysis of such a system. We propose and derive convergence estimates for a piecewise linear finite element method (FEM) with quadrature. We prove that the FEM is second order convergent for concentration in a discrete L 2 -norm. Since concentration depends on the gradient of acoustic pressure, this result shows that the FEM is superconvergent. Note that one expects the FEM to be convergent of order one in the L 2 -norm because the optimal convergence rate for the acoustic pressure is two in the H 1 -norm. We include numerical results backing the theoretical findings and an application of the model to a laboratory experiment of ultrasound enhanced transdermal drug delivery. [ABSTRACT FROM AUTHOR]

This paper presents a quasistatic problem of an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. We recall existence and uniqueness results obtained in Sofonea et al. (2017). The main aim of this paper is to present a fully discrete scheme for numerical approximation together with an error estimation of a solution to this problem. Finally, computational simulations are performed to illustrate the mathematical model. [ABSTRACT FROM AUTHOR]

In this paper we study from a mathematical point of view the drug release and the degradation process in the context of biodegradable intravitreal implants. In particular, two different clinical situations are considered: non-vitrectomized and vitrectomized eyes. In the former case we assume that the vitreous humor is replaced by a saline solution or a silicone oil. In intravitreal space, the intravitreal liquid enters the implant by non-Fickian diffusion causing the degradation of the poly(lactic-co-glycolic acid) based implant. Then, drug in the implant dissolves and diffuses out of the polymeric matrix. The transport of drug in the vitreous chamber and retina is modeled by Fickian diffusion and convection generated by the flow of the vitreous humor. In order to numerically solve the system of partial differential equations that define the model, we propose an Implicit–Explicit finite element method that allows for the decoupling of the solution reducing the computational cost of the simulations. Several numerical experiments showing the effectiveness of the proposed numerical schemes are also included. The proposed mathematical model may be useful to optimize patient specific treatments in clinical practice. • A model for degradation and drug delivery from a PLGA ocular implant is proposed. • The model studies the effects of the LA and GA into the break of the polymeric chains. • Humor diffuses into the implant creating a non-Fickian mass flux. • Drug release occurs by diffusion associated to humor absorption and dissolution. • Stability analysis of the fully couple model. [ABSTRACT FROM AUTHOR]

This paper deals with the spatial spreading speed and traveling wave solutions of a general epidemic model with nonlocal dispersal in time and space periodic habitats. It should be mentioned that the existence of spreading speed and traveling wave solutions of nonlocal dispersal cooperative system in space–time periodic habitats have been established previously. In this paper, we further show that the epidemic system has a spreading speed c ∗ ( ξ ) and for any c > c ∗ ( ξ ) , there exist a unique, continuous space–time periodic traveling wave solution ( Φ 1 ( x − c t ξ , t , c t ξ ) , Φ 2 ( x − c t ξ , t , c t ξ ) ) of epidemic model in the direction of ξ with speed c , and there is no such solution for c < c ∗ ( ξ ) . [ABSTRACT FROM AUTHOR]

This paper deals with a fully parabolic chemotaxis-growth system with singular sensitivity u t = Δ u − χ ∇ ⋅ u ∇ ln v + r u − μ u 2 , ( x , t ) ∈ Ω × ( 0 , ∞ ) , v t = Δ v − v + u , ( x , t ) ∈ Ω × ( 0 , ∞ ) , under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R 2 , where the parameters χ , μ > 0 and r ∈ R . Global existence and boundedness of solutions to the above system were established under some suitable conditions by Zhao and Zheng (2017). The main aim of this paper is further to show the large time behavior of global solutions which cannot be derived in the previous work. [ABSTRACT FROM AUTHOR]

In this paper, four meshless local weak form methods such as direct meshless local Petrov–Galerkin method (DMLPG), meshless local Petrov–Galerkin method (MLPG), local weak radial point interpolation method (LWRPIM) and local weak moving kriging method (LWMK) are applied to find the numerical solution of coupled non-linear advection–diffusion–reaction system arising in the prevention of groundwater contamination problem. A comparison between these methods is done from the perspective of accuracy and computational efficiency. An efficient fourth-order exponential time differencing Runge–Kutta method is utilized for the time discretization. The computational efficiency is the most significant advantage of the DMLPG method in comparison with the other meshless local weak form methods, because DMLPG reduces the computational costs, significantly. This is due to the fact that DMLPG shifts the numerical integrations over low-degree polynomials rather than over complicated shape functions. The main aim of this paper is to show that the meshless local weak form methods can be used for solving the system of non-linear partial differential equations especially coupled non-linear advection–diffusion–reaction system. The numerical results confirm the good efficiency of the proposed methods for solving our model. [ABSTRACT FROM AUTHOR]

This paper focuses on coupling two different computational approaches, namely finite element method (FEM) and meshless finite difference method (MFDM), in one domain. The coupled approach is applied in solving thermomechanical initial–boundary value problem where the heat transport in the domain is non-stationary. In this method, the domain is divided into two subdomains for FEM and MFDM, respectively. Contrary to other coupling techniques, the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level. In the weak form of thermomechanical initial–boundary value problem (variational principle), the appropriate additional coupling integrals are defined a-priori. Subsequently, the FEM and the MFDM approximations, which may differ from each other, are provided to the formulation. It is assumed that there exists a very thin layer of material between the subdomains, which is not spatially discretized. The width of this layer may be considered the coupling parameter and it is the same for both, thermal and mechanical parts. Similar approach is applied to essential boundary conditions (e.g. prescribed temperature and displacements). Consequently, the consistent formulation of the mixed problem for the coupled FEM–MFDM method is derived. The analysis is illustrated with two- and three-dimensional examples of mechanical and thermomechanical problems. [ABSTRACT FROM AUTHOR]

This paper describes iterative methods for the high frequency electromagnetic analysis using the finite element method of Maxwell equations including displacement current. The conjugate orthogonal conjugate gradient method has been widely used to solve a complex symmetric system. However, the conventional method suffers from oscillating convergence histories in large-scale analysis. In this paper, to solve large-scale complex symmetric systems arising from the formulation of the E method, an iterative substructuring method like the minimal residual method is presented, and the performance of the convergence of the method is evaluated by numerical results. As the result, the proposed method shows a stable convergence behavior and a fast convergence rate compared to other iterative methods. [ABSTRACT FROM AUTHOR]

In this paper we consider a mathematical model which describes a quasistatic process for a viscoelastic body in contact with an obstacle or a foundation. The variational formulation of the problem is in the form of a system coupling a nonlinear integral equation with a history-dependent hemivariational inequality. We establish a fully discrete scheme of the abstract problem and derive a result on error estimate. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the nonlinear system of cancer invasion model with haptotaxis effects in a bounded domain Ω ⊂ R n under the homogeneous Neumann and Robin type boundary conditions. This model also includes the growth and decay effects of cancer cells, normal cells and matrix degrading enzymes. This study devoted to estimate the lower bounds for the finite time blow up of non-negative solutions of the given cancer invasion system using first order differential inequality techniques and certain inequalities. [ABSTRACT FROM AUTHOR]

Abstract The notion of the Moore–Penrose inverse of a matrix has been extended to tensor case with Einstein product, recently. In this paper, we continue this work and propose the full rank decomposition of tensors by introducing a new kind of tensor rank, which gives a novel representation of the Moore–Penrose inverse. Moreover, we also obtain several formulae related to the Moore–Penrose inverse of a tensor and its { i , j , k } -inverses. In addition, we consider the tensor nearness problem associated with a tensor equation, a generalization of matrix nearness problems that arise in many areas of applied matrix computations. It is shown that the unique solution to the tensor nearness problem can be represented by using the Moore–Penrose inverses of the given tensors. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we use the parameterized single-step HSS (P-SHSS) iterative method to solve a broad class of singular complex symmetric linear systems. The semi-convergence properties of the P-SHSS method are derived under suitable conditions. Moreover, some properties of the preconditioned matrix and the optimal parameters are analyzed in detail. Numerical experiments are given to support our theoretical results and show the effectiveness of the P-SHSS method either as a solver or as a preconditioner. [ABSTRACT FROM AUTHOR]

Abstract The (1 ＋1)-dimensional mathematical model had been extensively derived to describe Rossby solitary waves in a line in the past few decades. But as is well known, the (1 ＋1)-dimensional model cannot reflect the generation and evolution of Rossby solitary waves in a plane. In this paper, a (2 ＋1)-dimensional nonlinear Zakharov–Kuznetsov–Burgers equation is derived to describe the evolution of Rossby wave amplitude by using methods of multiple scales and perturbation expansions from the quasi-geostrophic potential vorticity equations with the generalized beta effect. The effects of the generalized beta and dissipation are presented by the Zakharov–Kuznetsov–Burgers equation. We also obtain the new solitary solution of the Zakharov–Kuznetsov equation when the dissipation is absent with the help of the Bernoulli equation, which is different from the common classical solitary solution. Based on the solution, the features of the variable coefficient are discussed by geometric figures Meanwhile, the approximate solitary solution of Zakharov–Kuznetsov–Burgers equation is given by using the homotopy perturbation method. And the amplitude of solitary waves changing with time is depicted by figures. Undoubtedly, these solitary solutions will extend previous results and better help to explain the feature of Rossby solitary waves. [ABSTRACT FROM AUTHOR]

Abstract We present new linear energy-stable numerical schemes for numerical simulation of complex polymer–solvent mixtures. The mathematical model proposed by Zhou et al. (2006) consists of the Cahn–Hilliard equation which describes dynamics of the interface that separates polymer and solvent and the Oldroyd-B equations for the hydrodynamics of polymeric mixtures. The model is thermodynamically consistent and dissipates free energy. Our main goal in this paper is to derive numerical schemes for the polymer–solvent mixture model that are energy dissipative and efficient in time. To this end we will propose several problem-suited time discretizations yielding linear schemes and discuss their properties. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we establish a new regularity criterion for the two-dimensional incompressible generalized magnetohydrodynamics equations. [ABSTRACT FROM AUTHOR]

This paper presents a mathematically dynamic model of a Delta robot with flexible links. The mathematical models of the robot cannot be represented by partial differential equations, so this paper utilizes the kineto-elasto-dynamics and the finite element method to perform a mathematical model. Each link of the robot is modeled by multiple beam elements with an axial displacement, an axial torsion, and two transverse displacements. In literature, element assembling usually imposes a set of algebraic constraint equations, which are difficultly solved simultaneously. This paper proposes an alternative approach. A set of global variables based on the D–H method is defined, and the Euler–Lagrange’s equation is applied to derive the model without using any constraint equations. The developed model is a set of linear time-varying differential equations, which can describe the flexible motions with respect to the rigid body configuration. Furthermore, the natural frequency analysis and the convergence analysis are performed first, and then two types of paths are designed for the motions of the end-effector. The first path is a constant-speed circular motion in order to demonstrate the numerical simulations of the model at the steady state, and the second path is an inverted-U path, which is commonly used to operate a pick-to-place motion in industry. [ABSTRACT FROM AUTHOR]

The weather options were created to enable companies to hedge against climate risks. However, the valuation of weather options is complex, since the underlying temperature process has no negotiable price. This paper presents a new weather option pricing model, which is governed by a stochastic underlying temperature following a mean-reverting Browning motion with jump–diffusion under the assumption of mean-self-financing. Consequently, a two-dimensional partial integro-differential equation (PIDE) is derived to value the weather-based options. The numerical techniques applied in this paper are based on a Semi-Lagrangian method (SLM), in which at each time-step a set of one dimensional partial integro-differential equations are solved and the solution of each PIDE is updated using Semi-Lagrangian time-stepping. In addition, monotonicity, stability, and the convergence results of the discrete schemes are also derived in this paper. Lastly, this paper values a series of European HDD-based weather put options using SLM, and highlights the key details of the numerical implementation. [ABSTRACT FROM AUTHOR]

Sensitivity analysis is an important issue in large-scale mathematical modelling. We developed a novel 3-stage method for global sensitivity analysis of the Unified Danish Eulerian Model (UNI-DEM). This is a powerful large-scale air pollution model with an up-to-date high-performance software implementation. There is a number of uncertain internal parameters, especially in the chemistry–emission submodel, which are subject to our quantitative sensitivity study. Efficient Monte Carlo and quasi-Monte Carlo algorithms based on Sobol sequences are used in this study. A large number of numerical experiments with some special modifications of the model must be carried out in order to collect the necessary input data for the particular sensitivity study. For this purpose we created an efficient high performance implementation SA-DEM, based on the MPI version of the package UNI-DEM. A vast number of numerical experiments were carried out with SA-DEM on an IBM Blue Gene/P, the most powerful parallel supercomputer, at the time of the write-up of this paper, in Bulgaria. Even this powerful machine has some problems with the storage when SA-DEM is to be run with the refined (480×480) version of the mesh. The code was implemented with some enhancements on the IBM MareNostrum III at BSC — Barcelona, the most powerful parallel supercomputer in Spain. This implementation appears to be quite efficient for that challenging computational problem, as our experiments show. Some numerical results and performance analysis of these results will be presented in the paper. [ABSTRACT FROM AUTHOR]

Surface blending is a useful operation in geometric design for rounding sharp edges or corners. Meanwhile, NURBS has already become the de facto industrial standard in existing CAD/CAM systems. Therefore, it is required to study how to blend two B -spline surfaces. However, two arbitrary B -spline surfaces (called base surfaces ) are hard to be blended with a B -spline surface (called blending surface ) because the knot vectors of the two base surfaces are usually mismatched. In this paper, we proposed a curve-based spline representation, i.e., the semi-structured B-spline surface , which is generated by skinning a series of B -spline curves with different knot vectors. By assigning suitable knot vectors to the head and tail skinned curves, the semi-structured B -spline surface can blend two B -spline surfaces smoothly without disturbing them at all. We formulated the B -spline surface blending problem as an optimization problem with continuity constraints, and the continuity between the base and blending surfaces can reach G 2 or C 2 . Examples illustrated in this paper validate the effectiveness and efficiency of our method. [ABSTRACT FROM AUTHOR]

Recently a WENO scheme, with smoothness indicators constructed based on L 1 measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a diffusive epidemic model with nonlinear incidence rate under homogeneous Neumann boundary condition. The value of this study lies in two aspects. Mathematically, we show the stability of the constant positive steady state solution, the existence and nonexistence, the local and global structure of nonconstant positive steady states. And epidemiologically, we find that the system exhibits Turing patterns controlled by diffusion. [ABSTRACT FROM AUTHOR]

In this paper, we propose a spatial vaccination model with nonlinear incidence. First, we consider the well-posedness of solutions of the model. Second, in the case of the bounded spatial habitat Ω ⊆ R n , we investigate the global stability of the model. More precisely, it is shown that, if the threshold value R 0 ≤ 1 , then the disease-free equilibrium E 0 is globally asymptotically stable; if R 0 > 1 , then there exists a unique disease equilibrium E ∗ which is globally asymptotically stable. Third, in the case of the unbounded spatial habitat Ω = R n , we study the existence of traveling wave solutions of the model. Here we show that when the threshold value R 0 > 1 , then there exists c ∗ > 0 such that there exist positive traveling wave solutions of the model connecting the two equilibria E 0 and E ∗ with speed c > c ∗ . And when R 0 > 1 , there is not such a traveling wave solution with speed c < c ∗ . Numerical simulations are performed to illustrate our analytic results. Our results indicate that the global dynamics of the model are completely determined by the threshold value R 0 . [ABSTRACT FROM AUTHOR]

In this paper, an iterative method based on quasilinearization is presented to solve a class of two dimensional partial integro differential equations that arise in nuclear reactor models and population models. Two different approaches based on Haar and Legendre wavelets are studied to develop numerical methods. In the first approach, time domain is approximated with the help of forward finite difference approach. In the second approach, both time as well as space domains are approximated by wavelets. Appropriate examples are solved using these methods and the obtained results are compared with the methods available in the recent literature. [ABSTRACT FROM AUTHOR]

We are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models. In this paper, we formulate a computing technology to solve direct and inverse problems of atmospheric dynamics and chemistry. For the implementation, we use functional decomposition methods, splitting techniques, and integrating factors designed as the solutions of some adjoint problems. One of the main purposes of the paper is to relate the theory of approximation with the concept of Eulerian integrating factors that plays the fundamental role in the theory of differential equations. We demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection–diffusion (with dominant convection) and stiff systems of kinetic equations. To identify the prospects of our approach, we briefly introduce how to use integrating factors in the case of unstructured grids. [Copyright &y& Elsevier]

Abstract: This paper introduces a three dimensional (3D) thermal lattice Boltzmann method for the simulation of electron beam melting processes. The multi-distribution approach incorporates a state-of-the-art volume of fluid free surface method to handle the complex interaction between gas, liquid, and solid phases. The paper provides a detailed explanation of the modeling of the electron beam gun properties, such as the absorption rate and the energy dissipation. Additionally, an algorithm for the construction of a realistic powder bed is discussed. Special emphasis is placed to a parallel, optimized implementation due to the high computational costs of 3D simulations. Finally, a thorough validation of the heat equation and the solid–liquid phase transition demonstrates the capability of the approach to considerably improve the electron beam melting process. [Copyright &y& Elsevier]

Abstract: The pattern of some real phenomenon can be described by compartmental in-series models. Nevertheless, most of these processes are characterized by their variability, which produces that the exact values of the model parameters are uncertain, although they can be bounded by intervals. The aim of this paper is to compute tight solution envelopes that guarantee the inclusion of all possible behaviors of such processes. Current methods, such as monotonicity analysis, enable us to obtain guaranteed solution envelopes. However, if the model includes non-monotone compartments or parameters, the computation of solution envelopes may produce a significant overestimation. Our proposal consists of performing a change of variables in which the output is unaltered, and the model obtained is monotone with respect to the uncertain parameters. The monotonicity of the new system allows us to compute the output bounds for the original system without overestimation. These model transformations have been developed for linear and non-linear systems. Furthermore, if the conditions are not completely satisfied, a novel method to compute tight solution envelopes is proposed. The methods exposed in this paper have been applied to compute tight solution envelopes for two different models: a linear system for glucose modeling and a non-linear system for an epidemiological model. [Copyright &y& Elsevier]

Abstract: The aim of the paper is the description of fractional-order differential equations in terms of exact mechanical models. This result will be archived, in the paper, for the case of linear multiphase fractional hereditariness involving linear combinations of power-laws in relaxation/creep functions. The mechanical model corresponding to fractional-order differential equations is the extension of a recently introduced exact mechanical representation (Di Paola and Zingales (2012) [33] and Di Paola et al. (2012) [34]) of fractional-order integrals and derivatives. Some numerical applications have been reported in the paper to assess the capabilities of the model in terms of a peculiar arrangement of linear springs and dashpots. [Copyright &y& Elsevier]

This paper proves some regularity criteria for the 3D (density-dependent) incompressible Maxwell–Navier–Stokes system, which improves a recent result of Kang and Lee (2013). [ABSTRACT FROM AUTHOR]

In this paper, we develop a new dispersion minimizing finite difference scheme for the Helmholtz equation with perfectly matched layer (PML) in two dimensional domain, which is a second order 9-point scheme. To discretize the second derivative operator, we employ a linear combination of a point and its neighboring grid points to replace each of the five points in the traditional central difference scheme. Based on minimizing the numerical dispersion, the combination weights are determined by minimizing the numerical dispersion with a flexible selection strategy. The new scheme is simple, rotation-free, and pointwise consistent with the equation, which is different from the classical rotated 9-point difference scheme obtained by combining the Cartesian coordinate system and the rotated system. Moreover, it is a robust scheme even if the step sizes of different directions are not equal. Convergence analysis and dispersion analysis are given. Several numerical examples are presented to illustrate the numerical convergence and effectiveness of the new scheme. [ABSTRACT FROM AUTHOR]

In this paper, we study an inverse problem of parameters estimation for a new time-fractional heat conduction model in multilayered medium. In the anomalous thermal diffusion model, we consider the fractional derivative boundary conditions and the conduction obeys modified Fourier law with Riemann–Liouville fractional operator of different order in each layer. For the direct problem, we construct an effective finite difference scheme by using the balance method to deal with the discontinuity interface. For the inverse problem, we apply the nonlinear conjugate gradient (NCG) method with different conjugated coefficients to simultaneously identify the fractional exponent in each layer. Finally, we use experimental data to verify the effectiveness of the proposed technique, in which the Jacobian matrix is achieved by a derivative-free approach. We analyze the sensitivity coefficients and the convergence behaviors of the NCG algorithm. The simulation results confirm that the fractional heat conduction model with estimated parameters gives a more accurate fitting than the classical counterpart and the NCG method is a feasible and effective technique for the inverse problem of parameters estimation in fractional model. [ABSTRACT FROM AUTHOR]

Abstract: The paper presents a generalized model for quantifying and evaluating the survivability of systems and the services provided by the systems. For this purpose, we consider a multi-server system with infinite buffer, Markovian Arrival Process (MAP) and phase type (PH) service time distribution. The system is subject to the so-called propagated breakdowns. Accordingly, breakdowns arrive in bunches (we call them attacks) according to the MAP. Attacks consist of a random number of failures of different types defined by the required repair time. The process of arrival of different types of server failures within an attack is governed by phase type Markov process. The repair of a server takes an exponentially distributed time with intensity depending on the type of the occurred failure. We analyze the survivability of the system in terms of average time required for its complete recovery after an attack completion conditional no new attack arrives. In this paper, we consider two forms of recovery following the end of failure arrivals based on (1) the length of queue or (2) the number of broken servers reaching a preassigned level. To provide analysis of survivability, we first describe dynamics of the system by the multi-dimensional continuous time Markov chain. Then, we analyze survivability by means of matrix extension of so called method of collective marks. Numerical illustrations are also presented. [Copyright &y& Elsevier]

Abstract: Existing models from scheduling often over-simplify the problems appearing in real-world industrial situations. The original application is often reduced to a single-objective one, where the presence of uncertainty is neglected. In this paper, we focus on multi-objective optimization in uncertain environments. A bi-objective flowshop scheduling problem with uncertain processing times is considered. An indicator-based evolutionary algorithm is proposed to handle these two difficulties (multiple objectives and uncertain environment) at the same time. Four different strategies, based on uncertainty-handling quality indicators, are proposed in the paper. Computational experiments are performed on a large set of instances by considering different scenarios with respect to uncertainty. We show that an uncertainty-handling strategy is a key issue to obtain good-quality solutions, and that the algorithm performance is strongly related to the level of uncertainty over the environmental parameters. [Copyright &y& Elsevier]

Abstract: In this paper, we present a survivability evaluation model and analyze the performance of Wireless Sensor Networks (WSNs) under attack and key compromise. First, we present a survivability evaluation model of WSNs by representing the states of WSNs under attack. Here, the survivability of WSNs is expressed as a continuous time Markov Chain to describe the status of real WSNs. We propose a threshold condition to trigger the transition between the states of WSNs in the face of DoS attack. According to the threshold conditions, the survivability model is capable of taking action(s) and enables the formalization of the effect of action(s). We present an analytical model and numerical analysis to show the feasibility of our work in terms of availability, survivability, and cost. Second, we present a survivability model and evaluation of WSNs under key compromise. Sensor nodes in a network can be captured by an adversary. The compromised node can be identified by one of the intrusion detection mechanisms. After detecting the compromised node, the key in the node has to be revoked. In this paper, we present the effect of key compromise and key revocation in WSNs. We additionally present a survivability evaluation model using the SHARPE simulation tool in terms of availability. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximal methods for solving mixed general equilibrium bifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under some mild suitable conditions. Several cases are also discussed. Results in this paper include some new and known results as special cases. [Copyright &y& Elsevier]

Abstract: In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald–Letnikov discretization process which is easily implemented and reliably accurate. [Copyright &y& Elsevier]

Abstract: This paper has been motivated by the need to reduce the number of live animal tests in the development of an automated live-bird transfer system (LBTS) for the poultry meat-processing industry. Simulation-based models have been developed, which carefully address key engineering issues prior to live animal tests so that physical experiments can be focused on understanding reflex issues such as fear and escape behavior. To gain insights into the effects of operational timing on the LBTS handling performance, the multibody dynamics is modeled numerically based on the method of explicit dynamic finite element analysis (FEA) using off-the-shelf FEA packages. The findings also offer information on contact forces and their locations acting on the object’s body and legs by the compliant fingers and grippers respectively for optimizing designs and avoiding damage to the object. Specifically, this paper discusses computational issues such as time-step considerations and highly damped behavior of compliant fingers when modeling using dynamic FEA methods. The FEA model has been validated by comparing simulated handling of an ellipsoidal object by a pair of robotic hands with multiple compliant fingers against published experimental data. It is expected that the FEA-based method presented here can be extended to a spectrum of applications where flexible multibody dynamics involving large deformable contacts and highly damped behaviors plays an important role. [Copyright &y& Elsevier]

In this paper, we present an efficient adaptive mesh method for solving phase-field model of a mixture of two-phase incompressible fluid flows. The adaptive mesh is generated by a coordinate transformation that is determined as the solution of the classical problem of the optimal mass transportation, also known as Monge–Kantorovich problem (MKP). The numerical solution of the MKP is computed by taking the gradient of the steady state solution of a parabolic Monge–Ampère equation (PMAE). Several numerical experiments are conducted to demonstrate the performance of the PMAE method for solving phase-field models. The numerical results illustrate that the adaptive mesh computed with PMAE method captures well the moving interface of the phase-field function. [ABSTRACT FROM AUTHOR]

This paper deals with a delayed reaction–diffusion predator–prey model with non-smooth harvesting. Sufficient conditions for the local stability of the interior equilibrium and the existence of discontinuous Hopf bifurcations and classical Hopf bifurcations are obtained by using the theory of partial functional differential equations. Finally, numerical simulation results are presented to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of coupled viscoelastic equations with Dirichlet boundary conditions. We obtain a general decay result of solutions, which depends on the behavior of the relaxation functions and other given functions by using multiplier techniques and perturbed energy functional technique. [ABSTRACT FROM AUTHOR]

In this paper we analyze a discontinuous Galerkin finite element method for approximating solutions to transport equations with certain nonlinearities. We consider models for age-structured populations allowing for a nonlinear removal rate with non-local boundary conditions on the in-flow boundary. The method employs a stabilizing term over the interior edges allowing for convergence in a stronger than usual norm. We establish convergence rates for general higher order basis functions and provide numerical examples consistent with this result. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the Petri net (PN) based design and modeling approach for a periodic job-shop scheduling problem. Asynchronous synthesis for net-modules of the jobs is suggested in this paper for optimal allocation of shared resources to different operations. To make sure the completion of all the jobs in a single iteration of a production cycle and the correct calculation of a makespan, the synchronization problem among jobs is tackled by introducing the special synchronizing transition in the model. A timed-place PN is adopted for the purpose of finding the feasible schedule in terms of the firing sequence of the transitions of the PN model by using the heuristic search method. Further, the characterization of the PN model is performed and it is shown that the PN model for a periodic job-shop scheduling problem is equivalent to a class of PN known as parallel process net with resources (PPNRs). The modeling approach is demonstrated with a practical example and a makespan is calculated for the example. [Copyright &y& Elsevier]

Abstract: This paper presents a lattice Boltzmann method (LBM) based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non-body-fitted Cartesian meshes. The approach features (1) combining the interpolated bounce-back scheme with the LBM of multi-relaxation-time (MRT) type to enable the use of simple Cartesian mesh for the flow cases even with complex geometries; and (2) incorporating the Spalart–Allmaras (SA) turbulence model into LBM in order to represent the turbulent flow effect. The numerical experiments are performed corresponding to flows around an NACA0012 airfoil at Re=5×105 and around a flat plate at Re=2×104, respectively. The agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced LBM proposed in this paper for simulating, simply on Cartesian meshes, complex flows that may involve bodies of curved boundary, high Reynolds number, and large angle of attack. [Copyright &y& Elsevier]

Abstract: Proxy re-encryption (PRE) allows a semi-trusted proxy to convert a ciphertext originally intended for a user into another ciphertext of the same message intended for another user, and the proxy, however, cannot learn anything about the message encrypted. In previous papers, in order to achieve the CCA2-security, a common method for constructing PRE schemes was to apply the paradigm of using strongly-unforgeable one-time signature which transforms a selective-identity, CPA-secure identity-based encryption (IBE) scheme into a CCA-secure cryptosystem. In this paper, we propose a direct design of the bidirectional CCA-secure PRE scheme, which makes a direct use of the underlying IBE structure and does not need any auxiliary signature mechanism. Our construction is efficient and suitable for further designing multi-user PRE schemes. Its security is proved on the base of the decisional bilinear Diffie–Hellman assumption in the standard model. [Copyright &y& Elsevier]

Abstract: Uniform resampling is the easiest to apply and is a general recipe for all problems, but it may require a large replication size . To save computational effort in uniform resampling, balanced bootstrap resampling is proposed to change the bootstrap resampling plan. This resampling plan is effective for approximating the center of the bootstrap distribution. Therefore, this paper applies it to neural model selection. Numerical experiments indicate that it is possible to considerably reduce the replication size . Moreover, the efficiency of balanced bootstrap resampling is also discussed in this paper. [Copyright &y& Elsevier]

Abstract: This paper discusses the multinational capital budgeting problem — when there are some candidate foreign projects, which project(s) should the investor choose? In the paper, special cash flows and value sources of foreign projects are introduced. Regarding project parameters such as construction costs, annual net operating cash flows, terminal values of the projects as well as the foreign exchange rates as uncertain variables, the paper proposes one new uncertain zero–one integer model for optimal multinational project selection. To solve the problem, a hybrid intelligent algorithm integrating the 99 Methods and genetic algorithm is provided. As an illustration, an application example is also presented. [Copyright &y& Elsevier]

Abstract: Cardenas-Barron [L.E. Cardenas-Barron, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers and Industrial Engineering 57 (2009) 1105–1113] minimizes the annual total relevant cost to find the economic production quantity with rework process at a manufacturing system and assumes that is convex. So, the solution satisfying the first-order-derivative condition for will be the optimal solution. However, this paper indicates that does not necessarily exist although is convex. Consequently, the main purpose of this paper is two-fold: [(A)] This paper tries to develop the sufficient and necessary condition for the existence of the solution satisfying the-first-derivative condition of . [(B)] This paper tries to present a concrete solution procedure to find the optimal solution of . [Copyright &y& Elsevier]

Abstract: This paper deals with the Bloch equations which are a set of macroscopic equations that are used for modeling of nuclear magnetization as a function of time. These equations were introduced by Felix Bloch in 1946 and they are used for a description of the Nuclear Magnetic Resonance (NMR). This physical phenomenon is used in medicine, chemistry, physics, and engineering to study complex material. Fractional-order generalization of the Bloch equations was presented by Richard Magin et al. in 2008 as an opportunity to extend their use to describe a wider range of experimental situations involving heterogeneous, porous, or composite materials. In this paper we describe numerical and simulation models (created for Matlab/Simulink) of the classical and the fractional-order Bloch equations. The behaviour and stability analysis of the Bloch equations are presented as well. [ABSTRACT FROM AUTHOR]

Abstract: Learning and job deterioration co-exist in many realistic scheduling situations. This paper introduces a general scheduling model with the effects of learning and deterioration simultaneously which is a significant generalization of some existing models in the literature. By the effects of learning and deterioration, we mean that job processing times are defined by functions of their start times and positions in the sequence. This paper shows that the single-machine scheduling problems to minimize the makespan, sum of the th power of completion times, total lateness and sum of earliness penalties (with a common due date) are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time, discounted total weighted completion time, maximum lateness, maximum tardiness, total tardiness and total weighted earliness penalties (with a common due date) are polynomially solvable under certain conditions. [ABSTRACT FROM AUTHOR]