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Abstract: The problem of reconstructing signals and images from degraded ones is considered in this paper. The latter problem is formulated as a linear system whose coefficient matrix models the unknown point spread function and the right hand side represents the observed image. Moreover, the coefficient matrix is very ill-conditioned, requiring an additional regularization term. Different boundary conditions can be proposed. In this paper antireflective boundary conditions are considered. Since both sides of the linear system have uncertainties and the coefficient matrix is highly structured, the Regularized Structured Total Least Squares approach seems to be the more appropriate one to compute an approximation of the true signal/image. With the latter approach the original problem is formulated as an highly nonconvex one, and seldom can the global minimum be computed. It is shown that Regularized Structured Total Least Squares problems for antireflective boundary conditions can be decomposed into single variable subproblems by a discrete sine transform. Such subproblems are then transformed into one-dimensional unimodal real-valued minimization problems which can be solved globally. Some numerical examples show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper, a class of the direct methods for discretization of fractional order transfer functions is studied in the sense of stability preservation. The stability boundary curve is exactly determined for these discretization methods. Having this boundary helps us to recognize whether the original system and its discretized model are the same in the sense of stability. Finally, some illustrative examples are presented to evaluate achievements of the paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problem of model reduction for the linear port-controlled Hamiltonian systems. The development includes both the continuous- and discrete-time cases. Some sufficient conditions are obtained for the existence of solutions in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. In addition, an explicit parametrization of the desired reduced-order model can be constructed if these conditions are satisfied. Furthermore, the conditions based on the strict LMIs without rank constraint are derived for the zeroth-order approximation problem. Finally, the effectiveness of the proposed model reduction method is illustrated via a practical example. [Copyright &y& Elsevier]

Abstract: A burner configuration that allows the creation of nearly unstretched one-dimensional diffusion flames has recently been introduced. This paper presents the first detailed characterization of flames produced in such a burner to assess how well they approach the idealized one-dimensional configuration, which is used extensively for the development of theoretical models for diffusion flame stability. Particular emphasis is directed at quantifying the remaining inhomogeneities in the burner, such as residual flame stretch or variations in the boundary conditions, and identifying possible means to minimize them. Measurements made include the velocity field, stable species concentration profiles and temperature distribution throughout the burning chamber. Additionally, the flame position in the burner is determined as a function of mixture strength, reactant transport properties and bulk flow velocity. All the measurements are found to be in good agreement with a simplified one-dimensional flame model. However, the boundary conditions and their physical location have to be determined experimentally on both sides of the flame, which complicates comparison with results from theoretical and numerical models. Despite these limitations, we conclude that this new burner type provides a good experimental approximation of the one-dimensional idealized construct. [Copyright &y& Elsevier]

Abstract: The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a nonlinear two-point boundary value problem which is derived as a description of corneal shape. We prove some basic results concerning existence, uniqueness and estimates. We suggest some approximate solution fitting over fifteen thousands real corneal data points with an error of order of 1%. [Copyright &y& Elsevier]

Abstract: In this paper, a mathematical model of a tubular packed-bed catalytic reactor, which is modeled by a system of strongly nonlinear second-order partial differential equations with incompatible boundary conditions, will be solved. By properly using the boundary conditions and correctly choosing the solution search direction, approximate analytic solutions for the model can be obtained by the Adomian decomposition method. When the values of the dimensionless parameters in the system are assigned within a suitable range, the solutions describe objectively the distributions of the temperature and key reactant concentration in the reactor. [Copyright &y& Elsevier]

Abstract: Mathematical models for the release of drug from both non-degradable and degradable slab matrices in which the initial drug loading is greater than the solubility are presented in this paper. Taking the anomalous diffusions in the drug release processes into account, the fractional calculus is introduced to model the related phenomena. To describe different kinds of anomalous diffusions, corresponding fractional diffusion equations are adopted. By employing the integral transform methods, similarity solution method and perturbation method, exact and approximation solutions to the models are obtained. [Copyright &y& Elsevier]

Abstract: Fractional differentials provide more accurate models of systems under consideration. In this paper, approximation techniques based on the shifted Legendre-tau idea are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use. [Copyright &y& Elsevier]

Abstract: This paper studies a meshfree technique for the numerical solution of the two-dimensional reaction–diffusion Brusselator system along with Dirichlet and Neumann boundary conditions. Combination of collocation method using the radial basis functions (RBFs) with first order accurate forward difference approximation is employed for obtaining meshfree solution of the problem. Different types of RBFs are used for this purpose. The method is shown to converge to the only equilibrium point of the system. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the results obtained from the existing methods . The elementary stability analysis is established theoretically and is also supported by numerical results. [Copyright &y& Elsevier]

Abstract: In the present paper the finite element method for the solution of the eigenvalue problems for piezoelectric bodies with voids is considered. The porosity change properties are taken into account according to Cowin–Nunziato model. The vector–matrix formulations of the modal piezoelectric problems for media with voids are given. The finite element approximations of the continual equations are carried out and the finite dimensional eigenvalue problems are obtained in the expanded and in the various reduced forms. Algorithmic features of the boundary conditions account for electrode surfaces and the surfaces contacting with rigid stamps are discussed. The finite element eigenvalue problems for practically important electric resonance and antiresonance frequencies are obtained. As a numerical example the focusing spherical ultrasonic piezoelectric emitter fulfilled from porous piezoceramics is considered. With the use of Cowin–Nunziato model the effective moduli of the porous piezoceramic material are defined precisely. The results, which we obtain, show a good optimal agreement with the experimental data. The resonant frequency behavior modelling for free and loaded on acoustic media piezoelectric transducer is realized. [Copyright &y& Elsevier]

Abstract: In this paper we solve a system of second-order partial differential equations with non-standard boundary conditions. This system of equations is a mathematical model that describes distributions of the overpotential and reactant concentration in a working packed-bed electrode for an electrochemical reactor. To ensure the existence and uniqueness of the solutions for this model we choose standard instead of non-standard boundary conditions, and obtain approximate analytic solutions in the form of a series that rapidly converges using the Adomian decomposition method. The method is easily implemented using the symbol operations of scientific computational software such as MATLAB. [Copyright &y& Elsevier]

Abstract: In the present paper, static and dynamical problems for linearly elastic shells in curvilinear coordinates are considered. Hierarchies of two-dimensional models for corresponding boundary and initial boundary value problems are constructed within the variational settings. The existence and uniqueness of solutions of the reduced problems are investigated in suitable spaces. Under the conditions of solvability of the original static or dynamical problem, convergence of the sequence of vector functions of three variables restored from the solutions of the constructed two-dimensional problems to the solution of the three-dimensional problem is proved and approximation error is estimated. [Copyright &y& Elsevier]