Three‐point bending tests. Part II: An improved formula for the modulus of rupture and numerical simulations

The goal of this paper is to analyze analytical and numerically, from several perspectives, the modulus of rupture (MOR) for brittle materials, studying the bending test of three points which is normally used in laboratory to calculate it. In particular, we will give four different approaches to the MOR: through the classical theory of beams; by means of the one‐ and three‐dimensional numerical simulations; and by using an improved expression to the MOR obtained through its asymptotic analysis. Finally, we will present these methodologies for cylindrical and rectangular beams made of porcelain. Copyright © 2011 John Wiley & Sons, Ltd.     

Mathematical analysis of a viscoelastic problem with temperature‐dependent coefficients—Part I: Existence and uniqueness

The aim of this article is to study the quasistatic evolution of a thermoviscoelastic problem whose behaviour law is of the Maxwell–Norton type with coefficients depending on temperature. In this law, the deformation rate tensor is a superposition of viscoelastic and thermal contributions. The existence and uniqueness of the solution is proved. Copyright © 2007 John Wiley & Sons, Ltd.     

Mathematical analysis of a viscoelastic problem with temperature‐dependent coefficients—Part II: Regularity

In this paper, we study local regularity properties of the stress solution of a quasistatic thermoviscoelastic problem whose behaviour law is of the Maxwell–Norton type with temperature‐dependent coefficients. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth‐order integro‐differential equation

This paper presents general framework for solving the nth‐order integro‐differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation. Furthermore, in OHAM the convergence region can be easily adjusted and controlled. Comparison, via two examples, between our solution using HAM and OHAM and the exact solution shows that the HAM and the OHAM are effective and accurate in solving the nth‐order integro‐differential equation. Copyright © 2011 John Wiley & Sons, Ltd.     

Well‐posedness and asymptotic analysis for a Penrose–Fife type phase field system

In this paper, an asymptotic analysis of the (non‐conserved) Penrose–Fife phase field system for two vanishing time relaxation parameters ε and δ is developed, in analogy with the similar analyses for the phase field model proposed by G. Caginalp (Arch. Rational Mech. Anal. 1986; 92 :205–245), which were carried out by Rossi and Stoth (Adv. Math. Sci. Appl. 2003; 13 :249–271; Quart. Appl. Math. 1995; 53 :695–700). Although formally the singular limits for ε ↓ 0 and for ε and δ ↓ 0 are, respectively, the viscous Cahn–Hilliard equation and the Cahn–Hilliard equation, it turns out that the Penrose–Fife system is indeed a bad approximation for these equations. Therefore, we consider an alternative approximating phase field system, which could be viewed as a generalization of the classical Penrose–Fife phase field system, featuring a double non‐linearity given by two maximal monotone graphs. A well‐posedness result is proved for such a system, and it is shown that the solutions converge to the unique solution of the viscous Cahn–Hilliard equation as ε ↓ 0, and of the Cahn–Hilliard equation as ε ↓ 0 and δ ↓ 0. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical analysis for factorial data analysis. Part I: Numerical software — the package INDA for microcomputers

A large collection of factorial data analysis methods can be characterized by the following matrices: X , the k x n matrix of data, and A, B the symmetric positive definite matrices of size n, k which represent the chosen norms of ?ⁿ, ?^k, respectively. All methods amount to computing the largest eigenvalues of U = XAX^TB or the largest singular values of E = B^1/2XA^1/2 . In Part I of this paper we begin by a geometrical and probabilistic interpretation of the various methods, showing how U and E are defined in each case. We then define the computational kernel for factorial data analysis. We conclude by devising the numerical aspects of software implementation for this kernel on microcomputers and presenting the package INDA.     

Fundamental solutions and asymptotic numerical methods for bifurcation analysis of nonlinear bi‐harmonic problems

New algorithms, combining asymptotic numerical method (ANM) and method of fundamental solutions, are proposed to compute bifurcation points on branch solutions of a nonlinear bi‐harmonic problem. Three methods, mainly based on asymptotic developments framework, are then proposed. The first one consists in exploiting the ANM step accumulation close to the bifurcation points on a solution branch, the second method allows the introduction of an indicator that vanishes at the bifurcation points, and finally the first real root of the Padé approximant denominator represents the third bifurcation indicator. Two numerical examples are considered to analyze the robustness of these algorithms.     

Numerical and asymptotic study of non‐axisymmetric magnetohydrodynamic boundary layer stagnation‐point flows

Both numerical and asymptotic analyses are performed to study the similarity solutions of three‐dimensional boundary‐layer viscous stagnation point flow in the presence of a uniform magnetic field. The three‐dimensional boundary‐layer is analyzed in a non‐axisymmetric stagnation point flow, in which the flow is developed because of influence of both applied magnetic field and external mainstream flow. Two approaches for the governing equations are employed: the Keller‐box numerical simulations solving full nonlinear coupled system and a corresponding linearized system that is obtained under a far‐field behavior and in the limit of large shear‐to‐strain‐rate parameter (λ). From these two approaches, the flow phenomena reveals a rich structure of new family of solutions for various values of the magnetic number and λ. The various results for the wall stresses and the displacement thicknesses are presented along with some velocity profiles in both directions. The analysis discovered that the flow separation occurs in the secondary flow direction in the absence of magnetic field, and the flow separation disappears when the applied magnetic field is increased. The flow field is divided into a near‐field (due to viscous forces) and far‐field (due to mainstream flows), and the velocity profiles form because of an interaction between two regions. The magnetic field plays an important role in reducing the thickness of the boundary‐layer. A physical explanation for all observed phenomena is discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Comparative analysis of two asymptotic approaches based on integral manifolds

A comparative analysis of the two powerful asymptotic methods,ILDM and MIM (intrinsic low-dimensional manifolds; method ofinvariant manifold), is presented in the paper. The two methodsare based on the general theory of integral manifolds. The ILDMmethod is able to handle large systems of ODEs, whereas theMIM method treats systems with a limited number of unknown variables.The MIM method allows one to conduct analytical explorationof the original system and to obtain final expressions in compactform, whereas the ILDM method is a numerical approach that yieldsthe numerical form of the desired surface. The ILDM method workswell in a region where a rough splitting of the initial systemexists. Regions of the phase space where splitting does notexist are problematic for the ILDM method. In these regionsthe MIM method provides additional information regarding thedynamical behaviour of the system. A number of simple examplesare considered and analysed. It is shown that for the Semenovmodel (singularly perturbed system of ODEs) the ILDM methodgives a surface which appears close to the first order (withrespect to the corresponding small parameter) approximationof the stable (attracting) invariant manifolds. The complementaryproperties of the two asymptotic approaches suggests a feasiblecombination of the two methods, which is the subject of a futurework.     

Incompressible non‐Newtonian fluids: time asymptotic behaviour of weak solutions

We study the asymptotic behaviour in time of incompressible non‐Newtonian fluids in the whole space assuming that initial data also belong to L¹. Firstly, we consider the weak solution to the power‐law model with non‐zero external forces and we find the asymptotic behaviour in time of this solution in the same class of existence and uniqueness with p?. Secondly, we are interested in the asymptotic behaviour of weak solutions to the second grade model, and finally, we deal with the asymptotic behaviour in time of weak solutions to a simplified model of viscoelastic fluids of the Oldroyd type. Copyright © 2006 John Wiley & Sons, Ltd.     

Long‐time stability and asymptotic analysis of the IFE method for the multilayer porous wall model

In this article, we study the long‐time stability and asymptotic behavior of the immersed finite element (IFE) method for the multilayer porous wall model for the drug‐eluting stents. First, with the IFE method for the spatial descretization, and the implicit Euler scheme for the temporal discretization, respectively, we deduce the global stability of fully discrete solution. Then, we investigate the asymptotic behavior of the discrete scheme which reveals that the multilayer porous wall model converges to the corresponding elliptic equation if approaches to a steady‐state in both and norms as . Finally, some numerical experiments are given to verify the theoretical predictions.     

Linear relative canonical analysis of Euclidean random variables,asymptotic study and some applications

We introduce the Linear Relative Canonical Analysis (LRCA) of Euclidean random variables. Then similar properties than for usual linear Canonical Analysis are obtained. Furthermore, we develop an asymptotic study of LRCA and apply the obtained results to tests for lack of relative linear association, dimensionality and invariance.     

Kinetic models of chemotaxis towards the diffusive limit: asymptotic analysis

The paper is devoted to the study of the asymptotic behavior of the solutions of a kinetic model describing chemotaxis phenomena. Our interest focuses on the case, where the diffusion part dominates the chemotaxis part in the limit. More in detail, we prove that the solution of kinetic model exists globally and converges to a solution of diffusive limit. Copyright © 2015 John Wiley & Sons, Ltd.     

Uniqueness results,control and asymptotic analysis for slightly compressible fluids

We prove a unique continuation property for (weak) solutions of slightly compressible fluid equations. We deduce approximate controllability for such equations. We present the asymptotic analysis when the penalty's coefficient tends to infinity in control problems. Copyright © 1999 John Wiley & Sons, Ltd.     

Global asymptotic stability of CNNs with impulses and multi‐proportional delays

This paper is devoted to global asymptotic stability of cellular neural networks with impulses and multi‐proportional delays. First, by means of the transformation v_i(t) = u_i(e^t), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Second, we prove the global exponential stability of the latter by nonlinear measure, and that the exponential stability of the latter implies the asymptotic stability of the former. We furthermore provide a sufficient condition to the existence, uniqueness, and the global asymptotic stability of the equilibrium point of the former. Our results are generalizations of some existing ones. Finally, an example and its simulation are presented to illustrate effectiveness of our method. Copyright © 2015 John Wiley & Sons, Ltd.     

On a parabolic‐elliptic chemotaxis system with periodic asymptotic behavior

We study a parabolic‐elliptic chemotactic PDEs system, which describes the evolution of a biological population “u” and a chemical substance “v” in a bounded domain . We consider a growth term of logistic type in the equation of “u” in the form μu(1 ? u + f(t,x)). The function “f,” describing the resources of the systems, presents a periodic asymptotic behavior in the sense where f ^? is independent of x and periodic in time. We study the global existence of solutions and its asymptotic behavior. Under suitable assumptions on the initial data and f ^?, if the constant chemotactic sensitivity χ satisfies we obtain that the solution of the system converges to a homogeneous in space and periodic in time function.     

Global existence and asymptotic behavior of classical solutions for a 3D two‐species chemotaxis‐Stokes system with competitive kinetics

This paper considers the 2‐species chemotaxis‐Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a 3‐dimensional bounded domain with smooth boundary. Both chemotaxis‐fluid systems and 2‐species chemotaxis systems with competitive terms were studied by many mathematicians. However, there have not been rich results on coupled 2‐species–fluid systems. Recently, global existence and asymptotic stability in the above problem with (u·∇)u in the fluid equation were established in the 2‐dimensional case. The purpose of this paper is to give results for global existence, boundedness, and stabilization of solutions to the above system in the 3‐dimensional case when is sufficiently small.     

The global solvability and asymptotic behavior of a transmission problem for Kirchhoff‐type wave equations with memory source on the boundary

A transmission problem for Kirchhoff‐type wave equations with memory source term on one part of the boundary feedback is considered. By using the Faedo‐Galerkin approximation technique, the method of Lyapunov functional and the energy perturbation technique, we establish well‐posedness of global solution and derive a general decay estimate of the energy.     

Numerical analysis for factorial data analysis. Part II: Special purpose hardware—the programmable systolic array SARDA

The second part of this paper deals with the systolic implementation of the computational kernel for factorial data analysis, defined in Part I, on special-purpose hardware. The framework of the study is that a sequence of different algorithms has to be performed on a unique hardware array. This fact has led us to the design of the programmable systolic array SARDA: this is a triangular array which consists of programmable nodes with local memory and programmable orthogonal connections.