Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

A posteriori error estimates for a time discrete scheme for a phase-field system of Penrose-Fife type

A time discrete scheme is used to approximate the solution toa phase field system of Penrose–Fife type with a non-conservedorder parameter. An a posteriori error estimate is presentedthat allows the estimation of the difference between continuousand semidiscrete solutions by quantities that can be calculatedfrom the approximation and given data.     

Preparation and properties of the biodegradable graded blend of poly(L‐lactic acid) and poly(ethylene oxide)

We prepared biodegradable poly(ethylene oxide) (PEO)/poly(L ‐lactic acid) (PLLA) graded blends by the dissolution–diffusion process, and discussed the biodegradability and tensile strength of the graded blends by comparing isotropic blend and PLLA only. All the graded blends were degraded more largely than the PLLA only and isotropic blend (PEO: 37.5 wt %), which had the same content as the total content of those graded blends. The graded blend having most excellent wide compositional gradient was degraded most largely with the enzyme. Thus, graded structure of the blends promoted their biodegradabilities large. It was considered that the dissolution of PEO with water increased the surface area attacked by the enzyme, while PEO caught PLLA oligomers to promote the biodegradation of PLLA. Then, the biodegradabilities of the graded blends were suppressed by the increasing crystallinity of PLLA. Furthermore, the strengths of all the graded blends were larger than those of the isotropic blend. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2972–2981, 2007     

Microstructure dependent dynamic fracture analyses of trabecular bone based on nascent bone atomistic simulations

Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Primary constituents of trabecular tissue are hydroxyapatite (HA) mineralized type-I collagen fibers. In this research, dynamic fracture in two dimensional (2-D) micrographs of ovine (sheep) trabecular bone is modeled using the mesoscale cohesive finite element method (CFEM). The bone tissue fracture properties are obtained based on the atomistic strength analyses of a type-I collagen + HA interfacial arrangement using molecular dynamics (MD). Analyses show that the presented framework is capable of analyzing the architecture dependent fracture in 2-D micrographs of trabecular bone.     

Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.