Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Valorization of solid tire wastes available in Bangladesh by thermal treatment

In this study available solid tire wastes in Bangladesh were characterized through proximate and ultimate analyses, gross calorific values and thermogravimetric analysis to investigate their suitability as feedstock for thermal recycling by pyrolysis technology. A new approach in heating system, fixedbed fire-tube heating pyrolysis reactor has been designed and fabricated for the recovery of liquid hydrocarbons from solid tire wastes. The tire wastes were pyrolysed in the internally heated fixed-bed fire-tube heating reactor and maximum liquid yield of 46-55 wt% of solid tire waste was obtained at a temperature of 475 oC, feed size 4 cm3, with a residence time of 5 s under N2 atmosphere. The liquid products were characterized by physical properties, elemental analysis, FT-IR, 1H-NMR, GC MS techniques and distillation. The results show that the liquid products are comparable to petroleum fuels whereas fractional distillations and desulphurization are essential to be used as alternative for diesel engine fuels.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

Supramolecular selection in molecular alloys

Complexes of the type \[M(phen)3](PF6)2 (M = Ni(II), Fe(II), Ru(II) and phen = 1,10-phenanthroline) were found to co-crystallize to form molecular alloys (solid solutions of molecules) with general formula \[MAxMB1–x(phen)3](PF6)2·0.5H2O in which the relative concentrations of the metal complexes in the crystals closely match those in the crystallizing solution. Consequently, the composition of the co-crystals can be accurately predicted and controlled by modulating the relative concentrations of the metal complexes in the crystallizing solution. Although they are chemically and structurally similar, complexes of the type \[M(bipy)3](PF6)2 (M = Ni(II), Fe(II), Ru(II) and bipy = 2,2′-bipyridine) display markedly different behavior upon co-crystallization. In this case, the resulting co-crystals of general formula \[MAxMB1–x(bipy)3](PF6)2 have relative concentrations of the constituent complexes that are markedly different from the relative concentrations of the complexes initially present in the crystallizing solution. For example, when the nickel and iron complexes are co-crystallized from a solution containing a 50:50 ratio of each, the result is the formation of some crystals with a higher proportion of iron and others with a higher proportion of nickel. The relative concentrations of the metal complexes in the crystals can vary from those in the crystallizing solutions by as much as 15%. This result was observed for a range of combinations of metal complexes (Ni/Fe, Ni/Ru, and Fe/Ru) and a range of starting concentrations in the crystallizing solutions (90:10 through to 10:90 in 10% increments). To explain this remarkable result, we introduce the concept of “supramolecular selection”, which is a process driven by molecular recognition that leads to the partially selective aggregation of like molecules during crystallization.

From IKEA model to the lean construction concept: A solution to implementation

The productivity of the construction industry worldwide has been declining over the past forty years. One approach to improving the situation is by the introduction of lean construction. The IKEA model has also been shown to be beneficial when used in the construction context. A framework is developed in which the lean construction concept is embodied within the IKEA model by integrating Virtual Prototyping (VP) technology and its implementation is described and evaluated through a real-life case implementing the lean production philosophy. The operational flows of the IKEA model and lean construction are then compared to analyze the feasibility of IKEA-based lean construction. It is concluded that the successful application of the IKEA model in this context will promote the implementation of lean construction and improve the efficiency of the industry.

A coupled SPH-DEM model for fluid and solid mechanics of apple parenchyma cells during drying

A coupled SPH-DEM based two-dimensional (2-D) micro-scale single cell model is developed to predict basic cell-level shrinkage effects of apple parenchyma cells during air drying. In this newly developed drying model, Smoothed Particle Hydrodynamics (SPH) is used to model the low Reynolds Number fluid motions of the cell protoplasm, and a Discrete Element Method (DEM) is employed to simulate the polymer-like cell wall. Simulations results reasonably agree with published experimental drying results on cellular shrinkage properties such as cellular area, diameter and perimeter. These preliminary results indicate that the model is effective for the modelling and simulation of apple parenchyma cells during air drying.

The El Chichon stratospheric cloud : solid particulates and settling rates

Sampling of the El Chichón stratospheric cloud in early May and in late July, 1982, showed that a significant proportion of the cloud consisted of solid particles between 2 μm and 40 μm size. In addition, many particles may have been part of larger aggregates or clusters that ranged in size from < 10 μm to > 50 μm. The majority of individual grains were angular aluminosilicate glass shards with various amounts of smaller, adhering particles. Surface features on individual grains include sulfuric acid droplets and larger (0.5 μm to 1 μm) sulfate gel droplets with various amounts of Na, Mg, Ca and Fe. The sulfate gels probably formed by the interaction of sulfur-rich gases and solid particles within the cloud soon after eruption. Ca-sulfate laths may have formed by condensation within the plume during eruption, or alternatively, at a later stage by the reaction of sulfuric acid aerosols with ash fragments within the stratospheric cloud. A Wilson-Huang formulation for the settling rate of individual particles qualitatively agrees with the observed particle-size distribution for a period at least four months after injection of material into the stratosphere. This result emphasizes the importance of particle shape in controlling the settling rate of volcanic ash from the stratosphere.

Structural characterisation of kaolinite : NaCl intercalate and its derivatives

Kaolinite:NaCl intercalates with basal layer dimensions of 0.95 and 1.25 nm have been prepared by direct reaction of saturated aqueous NaCl solution with well-crystallized source clay KGa-1. The intercalates and their thermal decomposition products have been studied by XRD, solid-state 23Na, 27Al, and 29Si MAS NMR, and FTIR. Intercalate yield is enhanced by dry grinding of kaolinite with NaCl prior to intercalation. The layered structure survives dehydroxylation of the kaolinite at 500°–600°C and persists to above 800°C with a resultant tetrahedral aluminosilicate framework. Excess NaCl can be readily removed by rinsing with water, producing an XRD ‘amorphous’ material. Upon heating at 900°C this material converts to a well-crystallized framework aluminosilicate closely related to low-camegieite, NaAlSiO4, some 350°C below its stability field. Reaction mechanisms are discussed and structural models proposed for each of these novel materials.

A spectroscopic comparison of YBCO superconductors synthesised by solid-state and co-precipitation methods

Raman spectroscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM) have been used to compare samples of YBa2Cu3O7 (YBCO) synthesised by the solid-state method and a novel co-precipitation technique. XRD results indicate that YBCO prepared by these two methods are phase pure, however the Raman and SEM results show marked differences between these samples.

Imaging fluid solid interactions in hydrocarbon reservoir rocks

The environmental scanning electron microscope (ESEM) has been used to image liquid hydrocarbons in sandstones and oil shales. Additionally, the fluid sensitivity of selected clay minerals in hydrocarbon reservoirs was assessed via three case studies: HCl acid sensitivity of authigenic chlorite in sandstone reservoirs, freshwater sensitivity of authigenic illite/smectite in sandstone reservoirs, and bleach sensitivity of a volcanic reservoir containing abundant secondary chlorite/corrensite. The results showed the suitability of using ESEM for imaging liquid hydrocarbon films in hydrocarbon reservoirs and the importance of simulating in situ fluid-rock interactions for hydrocarbon production programmes. In each case, results of the ESEM studies greatly enhanced prediction of reservoir/borehole reactions and, in some cases, contradicted conventional wisdom regarding the outcome of potential engineering solutions. (C) 1993 Wiley-Liss, Inc.

Chemical vapor deposited boron carbide : growth by a vapor-liquid-solid process

Detailed analytical electron microscope (AEM) studies of yellow whiskers produced by chemical vapor deposition (CVD)1 show that two basic types of whiskers are produced at low temperatures (between 1200°C and 1400°C) and low boron to carbon gas ratios. Both whisker types show planar microstructures such as twin planes and stacking faults oriented parallel to, or at a rhombohedral angle to, the growth direction. For both whisker types, the presence of droplet-like terminations containing both Si and Ni indicate that the growth process during CVD is via a vapor-liquid-solid (VLS) mechanism.

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

A flexible solid-state pulsed power topology

Advances in solid-state switches and power electronics techniques have led to the development of compact, efficient and more reliable pulsed power systems. This paper proposes an efficient scheme that utilizes modular switch-capacitor units in obtaining high voltage levels with fast rise time (dv/dt) using low voltage solid-state switches. The proposed pulsed power supply has flexibility in terms of controlling energy and generating broad range of voltage levels. The energy flow can be controlled as the stored energy can be adjusted by a current source utilized at the first stage of the system. Desirable voltage level can be obtained by connecting adequate number of switch-capacitor units. Moreover, the proposed topology is load independent. Therefore it can easily supply wide range of applications especially the low impedance ones. The effectiveness of the proposed approach is verified by simulations