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     

Diffusion from sessile droplets through membranes

We analyze diffusion from a periodic array of hemispherical droplets through a membrane. We find that the multiple sources do not interact strongly, even when the droplets are closely spaced, so that the flux through the membrane appears nearly additive.     

Cosmic dust and our origins

The small solid particles in the space between the stars provide the surfaces for the production of many simple and complex molecules. Processes involving the effects of ultraviolet irradiation of the thin (hundredth micron) mantles are shown to produce a wide range of molecules and ions also seen in comets. Some of the more complex ones inferred from laboratory experiments are expected to play an important role in the origin of life. An outline of the chemical evolution of interstellar dust as observed and as studied in the laboratory is presented. Observations of comets are shown to provide substantial evidence for their being fluffy aggregates of interstellar dust as it was in the protosolar nebula, i.e. the interstellar cloud which collapsed to form the solar system. The theory that comets may have brought the progenitors of life to the earth is summarized.     

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     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

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.     

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     

Initial oxidation kinetics of copper (1 1 0) film investigated by in situ UHV-TEM

Previous studies of the initial stage of oxidation on clean single crystal of Cu(1 0 0) have been extended to the case of the Cu(1 1 0) surface. The dynamic observation of the nucleation and growth of Cu oxide by means of in situ ultra high vacuum transmission electron microscopy (UHV-TEM) shows a highly enhanced oxidation rate on Cu(1 1 0) surface as compared to Cu(1 0 0). The kinetic data on the nucleation and growth of the three-dimensional oxide islands agree well with our heteroepitaxial model of surface diffusion of oxygen.     

Strain hardening of polycarbonate in the glassy state: Influence of temperature and molecular weight

This study is concerned with the temperature and molecular weight dependence of the strain-hardening behavior of polycarbonate. It is shown that the strain-hardening modulus reduces with increasing temperature and decreasing molecular weight. This result is interpreted in terms of temperature accelerated relaxation of the entanglement network. Moreover, it is shown that frozen-in orientations, induced by homogeneous deformations above the glass transition temperature, lead to anisotropic yield behavior that can be fully rationalized (and modelled) in terms of a superimposed stress contribution of the prestrained network. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2041–2049, 2004     

Diffraction grating in noncrosslinked polymers

The diffraction efficiency and morphology of the transmission modes of holographic polymer dispersed liquid crystals were studied with respect to the molecular structure of poly(urethane acrylate) (PUA), the film (polymer/liquid crystal) and resin (oligomer/monomer) compositions, and the cell thickness. PUA, based on N‐vinylpyrrolidone and ethyl hexyl acrylate, with low‐molecular‐weight poly(propylene glycol) at a low oligomer content, showed high diffraction efficiency. The results were interpreted in terms of the monomer reactivity and polymer elasticity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 613–620, 2004