Search

Abstract: This paper derives fuzzy net present value (NPV) and pay back year (PBY) models as decision indexes for cogeneration alternatives decision-making. The Mellin transform is employed to establish the means and variances of the fuzzy indexes in order to rank various cogeneration alternatives. It is noted that the mean and variance values depend only on the vertexes of the fuzzy index, and are independent of their height. The current paper verifies the performance of the proposed models by simulating two numerical examples and by considering a cogeneration program in a petrochemical industry. It is shown that the results of the proposed fuzzy economic models are consistent with those of the conventional crisp models, and that the developed concepts are straightforward and easily implemented compared to the fuzzy ranking methods proposed in previous studies. Furthermore, the developed methods serve as readily implemented sensitivity analysis tools for use in the arena of uncertain decision-making. [Copyright &y& Elsevier]

This paper discusses the lot size-reorder point inventory problem with fuzzy demands. Different from the existing studies, the shortages are backordered with shortage cost incurred. The α cut of the fuzzy demand is used to construct the fuzzy total inventory cost for each inventory policy (Q, r), where Q is the quantity to be ordered and r is the reorder point. Yager''s ranking method for fuzzy numbers is utilized to find the best inventory policy in terms of the fuzzy total cost. Five pairs of simultaneous nonlinear equations for the optimal Q* and r* are derived for r in five different ranges of the fuzzy demand. When the demand is a trapezoidal fuzzy number, each pair of the simultaneous equations reduces to a set of closed-form equations. They are proved to be able to produce the optimal solution. Apparently, the methodology developed in this paper can be applied to other types of inventory problems to find the best inventory policy. [Copyright &y& Elsevier]

The single-period inventory models have wide applications in the real world in assisting the decision maker to determine the optimal quantity to order. Due to lack of historical data, the demand has to be subjectively determined in many cases. In this paper, a single-period inventory model for cases of fuzzy demand is constructed. The costs considered include the procurement cost, shortage cost, and holding cost. For different fuzzy total cost resulted from different order quantity, a method for ranking fuzzy numbers is adopted to find the optimal order quantity in terms of the cost. When the profit gained from selling one item is less (greater) than the loss incurred due to one unsold item, the optimal order quantity lies in the range defined for the left-shape (right-shape) function of the fuzzy demand. If the unit profit is equal to the unit loss, then all quantities with a membership grade 1 are optimal to be ordered. The methodology of this paper can be applied to construct other inventory models with fuzzy demand. [Copyright &y& Elsevier]

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]

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]

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]

We study global solutions of a class of chemotaxis–haptotaxis systems generalizing the prototype { u t = ∇ ⋅ ( ( u + 1 ) m − 1 ∇ u ) − ∇ ⋅ ( u ( u + 1 ) q − 1 ∇ v ) − ∇ ⋅ ( u ( u + 1 ) p − 1 ∇ w ) + H ( u , w ) , 0 = Δ v − v + u , w t = − v w , in a bounded domain Ω ⊂ R N ( N ≥ 1 ) with smooth boundary, H ( u , w ) : = u ( 1 − u r − 1 − w ) , with parameters m ≥ 1 , r > 1 and positive constants p , q . It is shown that either max { q + 1 , p , 2 p − m } < max { m + 2 N , r } or max { q + 1 , p , 2 p − m } = r and b > 0 is large enough, then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded. The results of this paper improve the results of Tao and Winkler (2014) [46,51]. [ABSTRACT FROM AUTHOR]

In this paper, efficient numerical schemes are proposed for solving the fractional water wave models that describe the propagation of surface water wave. By using the weighted and shifted Grünwald–Letnikov (WSGL) formula to approximate the nonlocal fractional operators, we design a series of second order accurate difference schemes for the considered models. The existence, stability and convergence of numerical solutions of the proposed numerical schemes are established rigorously. The analysis shows that the proposed numerical schemes are unconditionally stable with second order accuracy for both temporal and spatial discretizations. Several numerical results are provided to verify the efficiency and accuracy of our theoretical analysis. [ABSTRACT FROM AUTHOR]

The goal of this paper is to obtain a numerical approximation of the effective Hamiltonian for a system of PDEs deriving from a second order discrete model for traffic flow. We will propose an explicit and an implicit discretization for this effective Hamiltonian and we will provide the corresponding error estimates of Crandall–Lions type. Finally, we will also present some numerical simulations. [ABSTRACT FROM AUTHOR]

In the paper we consider the penalty finite element method for the stationary incompressible magnetohydrodynamics (MHD) problem with a factor of penalty parameter. Stability and convergence of numerical solutions are established. Furthermore, two level penalty methods are also developed for the MHD problem. Our methods consist of solving a nonlinear MHD problem by the usual penalty method on a coarse mesh with mesh size H , and then a linearized MHD problem based on the Stokes, Newton and Oseen iterations on a fine mesh is solved by the penalty method with mesh size h ( h ≪ H ) , respectively. Stability and error estimates of numerical solutions in two level penalty methods are presented. Finally, some numerical tests are provided to demonstrate the effectiveness of the developed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with positive solutions of a predator–prey model with Crowley–Martin functional response under Dirichlet boundary conditions. First, we establish the existence of positive solutions when ( a , c ) is close to ( λ 1 , λ 1 ) . Next, the stability properties of nonnegative solutions are discussed by spectral analysis. In addition, we obtain a complete understanding of the uniqueness and non-uniqueness of positive solutions by the Lyapunov–Schmidt procedure and the perturbation technique. At last, some numerical simulations are presented to supplement the analytic results in one dimension. [ABSTRACT FROM AUTHOR]

In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable of identifying a set of rules with a given strength and a given number of points. We also present polyquad which is an implementation of our methodology. Using polyquad v1.0 we proceed to derive a complete set of symmetric rules on the aforementioned domains. All rules possess purely positive weights and have all points inside the domain. Many of the rules appear to be new, and an improvement over those tabulated in the literature. [ABSTRACT FROM AUTHOR]

In this paper, 14-velocity and 18-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are proposed for three-dimensional incompressible flows. These two models are constructed based on the incompressible LBGK model proposed by He et al. (2004) and the MRT LB model proposed by d’Humières et al. (2002), which have advantages in the computational efficiency and stability, respectively. Through the Chapman–Enskog analysis, the models can recover to three-dimensional incompressible Navier–Stokes equations in the low Mach number limit. To verify the present models, the steady Poiseuille flow, unsteady pulsatile flow and lid-driven cavity flow in three dimensions are simulated. The simulation results agree well with the analytical solutions or the existing numerical results. Moreover, it is found that the present models show higher accuracy than d’Humières et al. model and better stability than He et al. model. [ABSTRACT FROM AUTHOR]

This paper proposes a new approximation method for conic sections by quartic Bézier curves with G 1 end-point continuity. We give an upper bound on the Hausdorff distance between the conic section and the quartic Bézier approximation curve, and also show that the approximation order is eight. Moreover, using the subdivision scheme at the shoulder point of the conic section, the resulting approximation curve has G 2 (curvature)-continuity with the conic section at the endpoints. Finally, we prove that our approximation has a smaller error bound than previous quartic Bézier approximations, and also present some numerical examples to demonstrate the validity and effectiveness of our method. [ABSTRACT FROM AUTHOR]

In the present paper we consider a 1D Poisson model characterized by the presence of an interface, where a transmission condition arises due to jumps of the coefficients. We aim at studying finite element methods with meshes not fitting such an interface. It is well known that when the mesh does not fit the material discontinuities the resulting scheme provides in general lower order accurate solutions. We focus on so-called embedded approaches, frequently adopted to treat fluid–structure interaction problems, with the aim of recovering higher order of approximation also in presence of non fitting meshes; we implement several methods inspired by: the Immersed Boundary method, the Fictitious Domain method, and the Extended Finite Element method. In particular, we present four formulations in a comprehensive and unified format, proposing several numerical tests and discussing their performance. Moreover, we point out issues that may be encountered in the generalization to higher dimensions and we comment on possible solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate all possible single traveling solitary wave solutions of the generalized KP–MEW equation ( u t − ( u 2 ) x − ( u 2 ) x x t ) x − u y y = 0 under boundary condition lim ξ → ± ∞ u ( ξ ) = A . Regular compacton solution of the generalized KP–MEW equation correspond to the case of A = 0 . In the case of A ≠ 0 , we find new exact soliton solutions including loop solution, cusped soliton, peaked soliton and smooth soliton solutions. The parametric conditions of existence of the loop solution, cusped soliton, peaked soliton, smooth soliton and compacton solutions are given by using the phase portrait analytical technique. Mathematical analysis and numerical simulations are provided for these soliton solutions of the generalized KP–MEW equation. We show some graphs to explain these solutions. [ABSTRACT FROM AUTHOR]

In this paper we consider a nonlinear heat equation with nonlinearities of variable-exponent type. We show that any solution with nontrivial initial datum blows up in finite time. We also give a two-dimension numerical example to illustrate our result. [ABSTRACT FROM AUTHOR]

This paper deals with the qualitative analysis of a nonlinear model of immune response with special attention to the actions applied by cytokine signals to activate the last one, in the framework of the mathematical kinetic theory for active particles. The content focuses on the early stage of the competition before the onset of proliferation. The analysis gives evidence how parameters and initial conditions influence the asymptotic behaviors of solutions. [ABSTRACT FROM AUTHOR]

In this article, the mathematical analysis of a model arising from biology consisting of diffusion, chemotaxis with volume filling effect and transport through an incompressible fluid, is studied. Motivated by numerical and modeling issues, the global-in-time existence of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of two-sidedly nonlinear degenerate diffusion and of anisotropic and heterogeneous diffusion tensors where we prove the global existence for a Chemotaxis-Navier–Stokes system in space dimensions less than or equal to four and we show the uniqueness of weak solutions for the Chemotaxis-Stokes system in two or three space dimensions under further assumptions. [ABSTRACT FROM AUTHOR]

In this paper, a control volume finite element scheme for the capture of spatial patterns for a volume-filling chemotaxis model is proposed and analyzed. The diffusion term, which generally involves an anisotropic and heterogeneous diffusion tensor, is discretized by piecewise linear conforming triangular finite elements (P1-FEM). The other terms are discretized by means of an upstream finite volume scheme on a dual mesh, where the dual volumes are constructed around the vertices of each element of the original mesh. The scheme ensures the validity of the discrete maximum principle under the assumption that the transmissibility coefficients are nonnegative. The convergence analysis is based on the establishment of a priori estimates on the cell density, these estimates lead to some compactness arguments in L 2 based on the use of the Kolmogorov compactness theorem. Finally, we show some numerical results to illustrate the effectiveness of the scheme to capture the pattern formation for the mathematical model. [ABSTRACT FROM AUTHOR]

Abstract: The stability is one of the most basic requirement for the numerical model, which is mostly elaborated for the linear problems. In this paper we analyze the stability notions for the nonlinear problems. We show that, in case of consistency, both the -stability and -stability notions guarantee the convergence. Moreover, by using the -stability we prove the convergence of the centralized Crank–Nicolson-method for the periodic initial-value transport equation. The -stability is applied for the investigation of the forward Euler method and the -method for the Cauchy problem with Lipschitzian right side. [Copyright &y& Elsevier]

Abstract: In this paper we propose a fast multiphase image segmentation model for gray images. Our proposed model is based on the piecewise constant multiphase Vese–Chan model, the globally convex segmentation method and the split Bregman method. Our proposed model has the advantages of the Vese–Chan model and can deal with piecewise constant multiphase images well. Besides, our proposed model is much more efficient than the Vese–Chan model by applying the globally convex segmentation method and the split Bregman method. We have tested our proposed model with many synthetic and real images. Experimental results have demonstrated the efficiency and robustness of our proposed model. [Copyright &y& Elsevier]

Abstract: This paper presents an enhancement to the free surface lattice Boltzmann method (FSLBM) for the simulation of bubbly flows including rupture and breakup of bubbles. The FSLBM uses a volume of fluid approach to reduce the problem of a liquid–gas two-phase flow to a single-phase free surface simulation. In bubbly flows compression effects leading to an increase or decrease of pressure in the suspended bubbles cannot be neglected. Therefore, the free surface simulation is augmented by a bubble model that supplies the missing information by tracking the topological changes of the free surface in the flow. The new model presented here is capable of handling the effects of bubble breakup and coalesce without causing a significant computational overhead. Thus, the enhanced bubble model extends the applicability of the FSLBM to a new range of practically relevant problems, like bubble formation and development in chemical reactors or foaming processes. [Copyright &y& Elsevier]

Abstract: The paper presents an unconditionally stable numerical scheme to solve a nonlinear integro-differential equation which arises in mathematical modeling of the penetration of a magnetic field into a substance, if the temperature is kept constant throughout the material. Numerical scheme comprises of the Galerkin finite element method (Jangveladze and Kiguradze, 2011) for the spatial discretization followed by an implicit finite difference scheme for the time stepping. We extended the results for stability estimates to a non homogeneous problem and derived optimal order error estimates for the semidiscretized and fully discretized equations using projection. Further, to show the efficiency, the proposed numerical method is demonstrated via numerical example. [Copyright &y& Elsevier]

Abstract: This paper is concerned with spatially homogeneous and inhomogeneous autocatalysis models with arbitrary order. For the spatially homogeneous model, the existence and stability of Hopf bifurcation surrounding the interior equilibrium are considered. For the model subject to zero-flux boundary conditions, Turing instability of the interior equilibrium is firstly discussed and Turing instability region regarding the diffusion coefficients is established. Then by the center manifold theory and normal form method, the existence of Hopf bifurcation and the stability of bifurcating periodic solutions are obtained, which is much more difficult and complicated than dealing with the spatially homogeneous case. Finally, to verify our analytical results, some examples of numerical simulations are also included. [Copyright &y& Elsevier]

Abstract: Many simple one-dimensional discrete models, for example, the Ricker and the logistic model, exhibit chaotic behaviour for large values of the map parameter . However, if a bounded stochastic perturbation with a positive expectation is introduced, for large, the map has a blurred asymptotically stable two-cycle, under some restrictions on the perturbation bounds and their mean. The paper considers two general types of maps including the Ricker and the truncated logistic model. It is demonstrated that bistability and multistability are possible, however, when perturbations are independent and identically distributed random variables and is large enough, trajectories eventually go into the blurred two-cycle with probability one. Moreover, with probability close to 1, there is a number starting from which all the trajectories are in the blurred two-cycle. [Copyright &y& Elsevier]

Abstract: Bayesian Networks are increasingly being used to model complex socio-economic systems by expert knowledge elicitation even when data is scarce or does not exist. In this paper, a Multi-Objective Evolutionary Algorithm (MOEA) is presented for assessing the parameters (input relevance/weights) of fuzzy dependence relationships in a Bayesian Network (BN). The MOEA was designed to include a hybrid model that combines Monte-Carlo simulation and fuzzy inference. The MOEA-based prototype assesses the input weights of fuzzy dependence relationships by learning from available output data. In socio-economic systems, the determination of how a specific input variable affects the expected results can be critical and it is still one of the most important challenges in Bayesian modeling. The MOEA was checked by estimating the migrant stock as a relevant variable in a BN model for forecasting remittances. For a specific year, results showed similar input weights than those given by economists but it is very computationally demanding. The proposed hybrid-approach is an efficient procedure to estimate output values in BN. [Copyright &y& Elsevier]

Abstract: Constructing the interval type-2 fuzzy sets (IT2 FSs) models is the essential step to realize computing with words (CWW) using IT2 FSs. This paper presents a novel strategy for the modeling of symmetric IT2 FSs using their uncertainty degrees. First, we provide the definition of uncertainty degree and the properties which show the reasonability of this uncertainty measure. Also, we derive the closed-form equations of the uncertainty degrees for the most widely-used symmetric Gaussian and trapezoidal IT2 FSs. Then, based on this uncertainty measure, we present one method to construct IT2 FS models using the uncertain interval end-points data. Finally, we apply the proposed IT2 FS modeling method to a real-world application—the thermal comfort modeling problem. This application demonstrated the usefulness of the proposed method on modeling words using IT2 FSs. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to develop a mathematical model to simulate mosquito dispersal and its control taking into account environmental parameters, like wind, temperature, or landscape elements. We particularly focus on the Aedes albopictus mosquito which is now recognized as a major vector of human arboviruses, like chikungunya, dengue, or yellow fever. One way to prevent those epidemics is to control the vector population. Biological control tools, like the Sterile Insect Technique (SIT), are of great interest as an alternative to chemical control tools which are very detrimental to the environment. The success of SIT is based not only on a good knowledge of the biology of the insect, but also on an accurate modeling of the insect’s distribution. We consider a compartmental approach and derive temporal and spatio-temporal models, using Advection–Diffusion–Reaction equations to model mosquito dispersal. Periodic releases of sterilized males are modeled with an impulse differential equation. Finally, using the splitting operator approach, and well-suited numerical methods for each operator, we provide numerical simulations for mosquito spreading, and test different vector control scenarios. We show that environmental parameters, like vegetation, can have a strong influence on mosquito distribution and in the efficiency of vector control tools, like SIT. [Copyright &y& Elsevier]

Abstract: The paper presents an exact formula for a Fourier series reconstruction of a function from its V-line Radon transform in a disc. This transform (often also called broken-ray Radon transform) appears in mathematical models of several imaging modalities, e.g. single-scattering optical tomography and -ray emission tomography. Our inversion formula relaxes the support restriction on the image function required in the previously discovered inversion technique (Ambartsoumian, 2012) [8], and uses data from only half of the set of broken rays required before. The general strategy of the current approach was outlined in (Ambartsoumian, 2012) [8]. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to present some homogenization results for a nonlinear problem arising in the modeling of diffusion in a periodic structure formed by two media with different properties, separated by an active interface. Our setting is relevant for modeling heat diffusion in composite materials with imperfect interfaces or electrical conduction in biological tissues. The approach we follow is based on the periodic unfolding method, which allows us to deal with general media. [Copyright &y& Elsevier]

Abstract: In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists of a coupled system of partial differential equations whose spatial domain is the tumor, that changes in size over time. Thus, the situation can be formulated as a free boundary problem. After solving the direct problem properly, we use the model for the estimation of parameters by fitting the numerical solution with real data, obtained via in vitro experiments and medical imaging. We define an appropriate functional to compare both the real data and the numerical solution. We use the adjoint method for the minimization of this functional. [Copyright &y& Elsevier]

Abstract: This paper deals with modeling and control of a hydraulic three-tank system. A process of creating a computer model in the MATLAB/Simulink environment is described, and optimal PID (proportional–integral–derivative) and model predictive controllers are proposed. The modeling starts with the creation of an initial mathematical model based on a first-principles approach. Then, the initial model is enhanced to obtain better correspondence with a real-time system, and parameters of the modified system are identified from measurements. The real-time system contains nonlinearities which cannot be neglected, and therefore are identified and included in the final mathematical model. The resulting model is used for a control design. As the real-time system has long time constants, usage of the Simulink model dramatically speeds up the design process. Optimal PID and model predictive controllers (MPC) are proposed and compared. Model predictive controllers for both a linearized model and the nonlinear system are proposed. The techniques described are not limited to one particular modeling problem, but can be used as an illustrative example for the modeling of many technological processes. [Copyright &y& Elsevier]

Abstract: This paper deals with the computation of nonlinear 2D transient magnetic fields when the data concerning the electric current sources involve potential drop excitations. In the first part, a mathematical model is stated, which is solved by an implicit time discretization scheme combined with a finite element method for space approximation. The second part focuses on developing a numerical method to compute periodic solutions by determining a suitable initial current which avoids large simulations to reach the steady state. This numerical method leads to solve a nonlinear system of equations which requires to approximate several nonlinear and linear magnetostatic problems. The proposed methods are first validated with an axisymmetric example and sinusoidal source having an analytical solution. Then, we show the saving in computational effort that this methodology offers to approximate practical problems specially with pulse-width modulation (PWM) voltage supply. [Copyright &y& Elsevier]

Abstract: Secret handshake (SH) schemes enable two members who belong to the same group to authenticate each other in a way that hides their affiliation to that group from all others. In previous work on SH, the group authority (GA) of the group G has been shown to have the ability to reveal the identity (ID) of a handshake player who belongs to G. The capability to reveal a malicious player is important in SH systems. In this paper, we focus first on the classification of traceability of GA. We classify this feature as follows: (i) GA of G is able to reveal IDs of members belonging to G by using a transcript of a handshake protocol; and (ii) GA of G is able to confirm whether handshake players belong to G or not by using a transcript of a handshake protocol. Previous research in this field only considers the former capability. In some situations, only the latter capability is needed. Next, we consider a SH system that GA has only an ability to confirm whether a handshake player belongs to his own group without revealing his ID. The most naive method is that member IDs are eliminated and members have a common group ID. However, if member ID does not exist, one cannot reveal the handshake player’s ID in the event of disputes. Thus, we introduce a SH with request-based-revealing (SHRBR). In SHRBR schemes, GA can check whether handshake players belong to their own group, but cannot reveal member IDs alone. After a handshake player executes a handshake protocol with , if wants to reveal a handshake partner (in this case ), requests GA to reveal a handshake partner’s ID by bringing forth his own ID and secret information of . We define the security requirements for SHRBR schemes and propose two concrete SHRBR schemes, SHRBR-1 and SHRBR-2. We prove that the proposed SHRBR schemes satisfy security requirements in the random oracle model. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the VIKOR method for dynamic intuitionistic fuzzy multiple attribute decision making (DIF-MADM). Two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are presented. Based on the DIFWA and UDIFWA operators respectively, we develop two procedures to solve the DIF-MADM problems where all attribute values are expressed in intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers, which are collected at different periods. Finally, a numerical example is used to illustrate the applicability of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper advanced variance-based algorithms for global sensitivity analysis are studied. We consider efficient algorithms, such as Monte Carlo, quasi-Monte Carlo (QMC) and scrambled quasi-Monte Carlo algorithms based on Sobol sequences. Low discrepancy Sobol sequences are considered as a basis. Two other approaches are also analyzed. The first one is an efficient Monte Carlo (MC) algorithm for multidimensional integration based on modified Sobol sequences (MCA-MSS) and proposed in an earlier work by some of the authors Dimov and Georgieva (2011) [28]. The second one is a randomized QMC algorithm proposed by Art Owen (1995) [20]. The procedure of randomization in the latter case is also known as Owen scrambling. The algorithms considered in this work are applied to sensitivity studies of air pollution levels calculated by the Unified Danish Eulerian Model (UNI-DEM) to some chemical reaction rates. UNI-DEM is chosen as a case study since it constitutes a typical large-scale mathematical model in which the chemical reactions are adequately presented. Extensive numerical experiments are performed to support the theoretical studies and to analyze applicability of algorithms under consideration to various classes of problems. Conclusions about the applicability and efficiency of the algorithms under consideration are drawn. [Copyright &y& Elsevier]

Abstract: A new scheme for implementing a reduced order model for complex mesh-based numerical models (e.g. finite element unstructured mesh models), is presented. The matrix and source term vector of the full model are projected onto the reduced bases. The proper orthogonal decomposition (POD) is used to form the reduced bases. The reduced order modeling code is simple to implement even with complex governing equations, discretization methods and nonlinear parameterizations. Importantly, the model order reduction code is independent of the implementation details of the full model code. For nonlinear problems, a perturbation approach is used to help accelerate the matrix equation assembly process based on the assumption that the discretized system of equations has a polynomial representation and can thus be created by a summation of pre-formed matrices. In this paper, by applying the new approach, the POD reduced order model is implemented on an unstructured mesh finite element fluid flow model, and is applied to 3D flows. The error between the full order finite element solution and the reduced order model POD solution is estimated. The feasibility and accuracy of the reduced order model applied to 3D fluid flows are demonstrated. [Copyright &y& Elsevier]

Abstract: The usage of models is a fundamental activity in designing and verifying a system. Mastering different modeling techniques and scaling their application to complex systems is not an easy task and requires both advanced skills and proper tools. One of the means that allow modelers to leverage the power of proper modeling techniques (e.g. stochastic techniques) is the application of abstractions by using high level formal modeling languages. This paper presents SIMTHESys, a framework for the development of formal modeling languages and the solution of multiformalism models by automatically generated solvers based on different solving engines. [Copyright &y& Elsevier]

Abstract: An effective exploration of the large search space by single population genetic-based metaheuristics may be a very time consuming and complex process, especially in the case of dynamic changes in the system states. Speeding up the search process by the metaheuristic parallelisation must have a significant negative impact on the search accuracy. There is still a lack of complete formal models for parallel genetic and evolutionary techniques, which might support the parameter setting and improve the whole (often very complex) structure management. In this paper, we define a mathematical model of Hierarchical Genetic Search (HGS) based on the genetic multi-agent system paradigm. The model has a decentralised population management mechanism and the relationship among the parallel genetic processes has a multi-level tree structure. Each process in this tree is Markov-type and the conditions of the commutation of the Markovian kernels in HGS branches are formulated. [Copyright &y& Elsevier]

Abstract: The paper is devoted to the computational time-domain formulation of linear viscoelastic systems submitted to a nonstationary stochastic excitation and in the presence of model uncertainties which are modeled in the framework of the probability theory. The objective is to introduce and to develop an adapted and complete formulation of such a problem in the context of computational mechanics. A reduced-order model in the time domain with stochastic excitation is derived from the computational model. For the reduced-order model, the stochastic modeling of both computational model-parameter uncertainties and modeling errors is carried out using the nonparametric probabilistic approach and the random matrix theory. We present a new formulation of model uncertainties to construct the random operators for viscoelastic media. We then obtained a linear Stochastic Integro-Differential Equation (SIDE) with random operators and with a stochastic nonhomogeneous part (stochastic excitation). A time discretization of this SIDE is proposed. In a first step, the SIDE is transformed to a linear Itô Stochastic Differential Equation (ISDE) with random operators. Then the ISDE is discretized using an extension of the Störmer–Verlet scheme which is a particularly well adapted algorithm for long-time good behavior of the numerical solution. Finally, for the stochastic solver and statistical estimations of the random responses, we propose to use the Monte Carlo simulation for Gaussian and non-Gaussian excitations. [Copyright &y& Elsevier]

Abstract: This paper studies fractional variable structure controllers. Two cases are considered namely, the sliding reference model and the control action, that are generalized from integer into fractional orders. The test bed consists in a mechanical manipulator and the effect of the fractional approach upon the system performance is evaluated. The results show that fractional dynamics, both in the switching surface and the control law are important design algorithms in variable structure controllers. [Copyright &y& Elsevier]