Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Semiclassical equations for weakly inhomogeneous cosmologies

The in-in effective action formalism is used to derive the semiclassical correction to Einsteins equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological models. The vacuum expectation value of the stress tensor of the quantum field is directly derived from the renormalized in-in effective action. The usual in-out effective action is also discussed and it is used to compute the probability of particle creation. As one application, the stress tensor of a scalar field around a static cosmic string is derived and the back-reaction effect on the gravitational field of the string is discussed.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Failure in composite materials

The economic and efficient exploitation of composite materials in critical load bearing applications relies on the ability to predict safe operational lives without excessive conservatism. Developing life prediction and monitoring techniques in these complex, inhomogeneous materials requires an understanding of the various failure mechanisms which can take place. This article describes a range of damage mechanisms which are observed in polymer, metal and ceramic matrix composites.

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Asymmetric reversal in inhomogeneous magnetic heterostructures

Asymmetric magnetization reversal is an unusual phenomenon in antiferromagnet/ferromagnet (AF/FM) exchange biased bilayers. We investigated this phenomenon in a simple model system experimentally and by simulation assuming inhomogeneously distributed interfacial AF moments. The results suggest that the observed asymmetry originates from the intrinsic broken symmetry of the system, which results in local incomplete domain walls parallel to the interface in reversal to negative saturation of the FM. The magneto-optical Kerr effect unambiguously confirms such an asymmetric reversal and a depth-dependent FM domain wall in accord with the magnetometry and simulations.

The role of potassium in the corrosion of superheater materials in boilers firing biomass

Inhibition of global warming has become one of the major goals for the coming decades. A key strategy is to replace fossil fuels with more sustainable fuels, which has generated growing interest in the use of waste-derived fuels and of biomass fuels. However, from the chemical point of view, biomass is an inhomogeneous fuel, usually with a high concentration of water and considerable amounts of potassium and chlorine, all of which are known to affect the durability of superheater tubes. To slow down or reduce corrosion, power plants using biomass as fuel have been forced to operate at lower steam temperatures as compared to fossil fuel power plants. This reduces power production efficiency: every 10°C rise in the steam temperature results in an approximate increase of 2% in power production efficiency. More efficient ways to prevent corrosion are needed so that power plants using biomass and waste-derived fuels can operate at higher steam temperatures. The aim of this work was to shed more light on the alkali-induced corrosion of superheater steels at elevated temperatures, focusing on potassium chloride, the alkali salt most frequently encountered in biomass combustion, and on potassium carbonate, another potassium salt occasionally found in fly ash. The mechanisms of the reactions between various corrosive compounds and steels were investigated. Based on the results, the potassium-induced accelerated oxidation of chromia protected steels appears to occur in two consecutive stages. In the first, the protective chromium oxide layer is destroyed through a reaction with potassium leading to the formation of intermediates such as potassium chromate (K2CrO4) and depleting the chromium in the protective oxide layer. As the chromium is depleted, chromium from the bulk steel diffuses into the oxide layer to replenish it. In this stage, the ability of the material to withstand corrosion depends on the chromium content (which affects how long it takes the chromium in the oxide layer to be depleted) and on external factors such as temperature (which affects how fast the chromium diffuses into the protective oxide from the bulk steel). For accelerated oxidation to continue, the presence of chloride appears to be essential.

Effect of spin-polarized subbands in the inhomogeneous hole gas providing the indirect exchange in GaMnAs bilayers

The magnetic order resulting from the indirect exchange in the metallic phase of a (Ga,Mn)As/GaAs double layer structure is studied via Monte Carlo simulation. The polarization of the hole gas is taken into account, establishing a self-consistency between the magnetic order and the electronic structure. The Curie-Weiss temperatures calculated for these low-dimensional systems are in the range of 50-80 K, and the dependence of the transition temperature with the GaAs separation layer is established. (C) 2003 Published by Elsevier B.V.

Fractal approach to ac impedance spectroscopy studies of ceramic materials

A novel fractal model for grain boundary regions of ceramic materials was developed. The model considers laterally inhomogeneous distribution of charge carriers in the vicinity of grain boundaries as the main cause of the non-Debye behaviour and distribution of relaxation times in ceramic materials. Considering the equivalent circuit the impedance of the grain boundary region was expressed. It was shown that the impedance of the grain boundary region has the form of the Davidson-Cole equation. The fractal dimension of the inhomogeneous distribution of charge carriers in the region close to the grain boundaries could be calculated based on the relation ds = 1 + β, where β is the constant from the Davidson-Cole equation.

Structure and properties of composite polyolefin materials

This thesis is based on three main studies, all dealing with structure-property investigation of semicrystalline polyolefin-based composites. Low density poly(ethylene) (LDPE) and isotactic poly(propylene) (iPP) were chosen as parts of the composites materials and they were investigated either separately (as homoploymers), either in blend systems with the composition LDPE/iPP 80/20 or as filled matrix with layered silicate (montmorillonite). The beneficial influence of adding ethylene-co-propylene polymer of amorphous nature, to low density poly(ethylene)/isotactic poly(propylene) (80/20) blend is demonstrated. This effect is expressed by the major improvement of mechanical properties of ternary blends as examined at a macroscopic size scale by means of tensile measurements. The structure investigation also reveals a clear dependence of the morphology on adding ethylene-copropylene polymer. Both the nature and the content of ethylene-co-propylene polymer affect structure and properties. It is further demonstrated that the extent of improvement in mechanical properties is to be related to the molecular details of the compatibilizer. Combination of high molecular weight and high ethylene content is appropriate for the studied system where the poly(ethylene) plays the role of matrix. A new way to characterize semicrystalline systems by means of Brillouin spectroscopy is presented in this study. By this method based on inelastic light scattering, we were able to measure the high frequency elastic constant (c11) of the two microphases in the case where the spherulites size is exhibit size larger than the size of the probing phonon wavelength. In this considered case, the sample film is inhomogeneous over the relevant length scales and there is an access to the transverse phonon in the crystalline phase yielding the elastic constant c44 as well. Isotactic poly(propylene) is well suited for this type of investigation since its morphology can be tailored through different thermal treatment from the melt. Two distinctly different types of films were used; quenched (low crystallinity) and annealed (high crystallinity). The Brillouin scattering data are discussed with respect to the spherulites size, lamellae thickness, long period, crystallinity degree and well documented by AFM images. The structure and the properties of isotactic poly(propylene) matrix modified by inorganic layered silicate, montmorillonite, are discussed with respect to the clay content. Isotactic poly(propylene)-graft-maleic anhydride was used as compatibilizer. It is clearly demonstrated that the property enhancement is largely due to the ability of layered silicate to exfoliate. The intimate dispersion of the nanometer-thick silicate result from a delicate balance of the content ratio between the isotactic poly(propylene)-graft-maleic anhydride compatibilizer and the inorganic clay.

Microwave properties of an inhomogeneous optically illuminated plasma in a microstrip gap

The optical illumination of a microstrip gap on a thick semiconductor substrate creates an inhomogeneous electron-hole plasma in the gap region. This allows the study of the propagation mechanism through the plasma region. This paper uses a multilayer plasma model to explain the origin of high losses in such structures. Measured results are shown up to 50 GHz and show good agreement with the simulated multilayer model. The model also allows the estimation of certain key parameters of the plasma, such as carrier density and diffusion length, which are difficult to measure by direct means. The detailed model validation performed here will enable the design of more complex microwave structures based on this architecture. While this paper focuses on monocrystalline silicon as the substrate, the model is easily adaptable to other semiconductor materials such as GaAs.

Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

Linear dimensional changes in plaster die models using different elastomeric materials

Dental impression is an important step in the preparation of prostheses since it provides the reproduction of anatomic and surface details of teeth and adjacent structures. The objective of this study was to evaluate the linear dimensional alterations in gypsum dies obtained with different elastomeric materials, using a resin coping impression technique with individual shells. A master cast made of stainless steel with fixed prosthesis characteristics with two prepared abutment teeth was used to obtain the impressions. References points (A, B, C, D, E and F) were recorded on the occlusal and buccal surfaces of abutments to register the distances. The impressions were obtained using the following materials: polyether, mercaptan-polysulfide, addition silicone, and condensation silicone. The transfer impressions were made with custom trays and an irreversible hydrocolloid material and were poured with type IV gypsum. The distances between identified points in gypsum dies were measured using an optical microscope and the results were statistically analyzed by ANOVA (p < 0.05) and Tukey's test. The mean of the distances were registered as follows: addition silicone (AB = 13.6 µm, CD=15.0 µm, EF = 14.6 µm, GH=15.2 µm), mercaptan-polysulfide (AB = 36.0 µm, CD = 36.0 µm, EF = 39.6 µm, GH = 40.6 µm), polyether (AB = 35.2 µm, CD = 35.6 µm, EF = 39.4 µm, GH = 41.4 µm) and condensation silicone (AB = 69.2 µm, CD = 71.0 µm, EF = 80.6 µm, GH = 81.2 µm). All of the measurements found in gypsum dies were compared to those of a master cast. The results demonstrated that the addition silicone provides the best stability of the compounds tested, followed by polyether, polysulfide and condensation silicone. No statistical differences were obtained between polyether and mercaptan-polysulfide materials.

Subcutaneous connective tissue response to primary root canal filling materials

This study evaluated the response of the subcutaneous connective tissue of BALB/c mice to root filling materials indicated for primary teeth: zinc oxide/eugenol cement (ZOE), Calen paste thickened with zinc oxide (Calen/ZO) and Sealapex sealer. The mice (n=102) received polyethylene tube implants with the materials, thereby forming 11 groups, as follows: I, II, III: Calen/ZO for 7, 21 and 63 days, respectively; IV, V, VI: Sealapex for 7, 21 and 63 days, respectively; VII, VIII, IX: ZOE for 7, 21 and 63 days, respectively; X and XI: empty tube for 7 and 21 days, respectively. The biopsied tissues were submitted to histological analysis (descriptive analysis and semi-quantitative analysis using a scoring system for collagen fiber formation, tissue thickness and inflammatory infiltrate). A quantitative analysis was performed by measuring the area and thickness of the granulomatous reactionary tissue (GRT). Data were analyzed by Kruskal-Wallis, ANOVA and Tukey's post-hoc tests (?=0.05). There was no significant difference (p>0.05) among the materials with respect to collagen fiber formation or GRT thickness. However, Calen/ZO produced the least severe inflammatory infiltrate (p<0.05). The area of the GRT was significantly smaller (p<0.05) for Calen/ZO and Sealapex. In conclusion, Calen/ZO presented the best tissue reaction, followed by Sealapex and ZOE.