An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for <svg style="vertical-align:-0.0pt;width:18.65px;" id="M1" height="10.6875" version="1.1" viewBox="0 0 18.65 10.6875" width="18.65"  xmlns="http://www.w3.org/2000/svg">
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</svg> values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given.  Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.

M. Emin Erdo&#287;an

C. Erdem &#304;mrak

Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls

Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.

A. Hmamed

M. Alfidi

A. Benzaouia

F. Tadeo

LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems

Huxley equation is a core mathematical framework for modern biophysically based neural modeling. It is often useful to obtain a generalized solitary solution for fully understanding its physical meanings. There are many methods to solve the equation, but each method can only lead to a special solution. This paper suggests a relatively new method called the Exp-function method for this purpose. The obtained result includes all solutions in open literature as special cases, and the generalized solution with some free parameters might imply some fascinating meanings hidden in Huxley equation.

Xin-Wei Zhou

Exp-Function Method for Solving Huxley Equation

Solution of a nonlinear two-point boundary value problem is studied using variational iteration method (VIM) considering its convergence behavior due to the changing nonlinearity effects in the equation. To achieve this, steady Burger equation is first solved by using finite element method (FEM) with a very fine mesh for the comparison of results obtained from VIM. Effect of the nonlinear term in the equation that is multiplied by a constant is taken into account for five different cases by changing the corresponding constant. Results have shown that VIM is a flexible, easy to apply, and promising method for the analysis of nonlinear two-point boundary value problems with the fact that the larger the effect of the nonlinear term of the equation, the slower the convergence rate when compared to FEM solutions.

MehmetTar&#x131;k Atay

SafaBozkurt Co&#x15F;kun

Effects of Nonlinearity on the Variational Iteration Solutions of Nonlinear Two-Point Boundary Value Problems with Comparison with Respect to Finite Element Analysis

In this work, two numerical methodologies are proposed for the solution of unilateral contact problems between a structural member (beam or arch) and an elastic foundation. In the first approach, the finite element method is used to discretize the structure and elastic foundation and the contact problem is formulated as a constrained optimization problem. Only the original variables of the problem are used, subjected to inequality constraints, and the relevant equations are written as a linear complementary problem (LCP). The second approach is based on the Ritz method, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem. The contact problem here is treated as an unconstrained optimum design problem. These proposed methodologies are then tested and compared using results from specific problems involving structures under unilateral contact constraints.

Ricardo A. M. Silveira

Wellington L. A. Pereira

Paulo B. Gonçalves

Constrained and Unconstrained Optimization Formulations for Structural Elements in Unilateral Contact with an Elastic Foundation

A method is presented for computation of positive realizations for given impulse response matrices of discrete-time systems. Sufficient conditions for the existence of positive realizations are established and a procedure for computation of positive realizations for given impulse response matrices is proposed.

Tadeusz Kaczorek

Computation of Positive Realizations for Given Impulse Response Matrices of Discrete-Time Systems

When engineers model the magnetostatic fields applied to recording
heads of computer hard drives due to a magnetic recording medium,
the solution of Laplace&#39;s equation must be found. A popular solution
method is based on Fourier analysis. However, due to the geometry of
the read head model, an interesting mathematical problem arises. The
coefficients for the Fourier series solution of the desired magnetic
potential satisfy an infinite system of linear equations. In
practice, the infinite system is truncated to a finite system with
little consideration for the effect this truncation has on the
solution. The paper will provide a proper understanding of the
underlying problem and a formal analysis of the effect of
truncation.

John L. Fleming

Convergence Analysis of a Fourier-Based Solution Method 
      of the Laplace Equation for a Model of Magnetic Recording

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<p><em>Mathematical Problems in Engineering</em> is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.</p>


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<p>Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.</p>


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Mathematical Problems in Engineering