The enclosure method for the heat equation

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary value problems whose governing equation is the heat equation is considered. An explicit method to extract an approximation of the value of the support function at a given direction of unknown discontinuity embedded in a heat conductive body from the temperature for a suitable heat flux on the lateral boundary for a fixed observation time is given.Comment: 12pages. This is the final versio

Harmonic moments and an inverse problem for the heat equation

In the paper, we study an inverse problem for the heat equation. We introduce a class of bilinear forms on the space of harmonic polynomials ( called harmonic moments), which are represented by the Dirichlet-to-Neumann map. We investigate the uniqueness, stability, and reconstruction of the inverse problem. The inverse data are given in the terms of the bilinear forms and can be exchanged into the data of the Dirichlet-to-Neumann map. The reconstruction ( of the density) is accomplished in two different ways: one is due to the idea of the mollifier and the other to the representation by the Carleman kernel in the complex analysis. The error terms are estimated depending on the degree of the harmonic polynomials. We estimates norms of the data on an arbitrary time interval by the norms on some fixed interval (e.g., 0 < t < 2)

Biomimetic apatite formation on different polymeric microspheres modified with calcium silicate solutions

Proceedings of the 18th International Symposium on Ceramics in Medicine, The Annual Meeting of the International Society for Ceramics in Medicine (ISCM), Kyoto, Japan, 5-8 December 2005. Published in : Key Enggineering Materials, vol. 309 - 311Bioactive polymeric microspheres can be produced by pre-coating them with a calcium silicate solution and the subsequent soaking in a simulated body fluid (SBF). Such combination should allow for the development of bioactive microspheres for several applications in the medical field including tissue engineering. In this work, three types of polymeric microspheres with different sizes were used: (i) ethylene-vinyl alcohol co-polymer (20-30 'm), (ii) polyamide 12 (10-30 'm) and (iii) polyamide 12 (300 'm). These microspheres were soaked in a calcium silicate solution at 36.5ºC for different periods of time under several conditions. Afterwards, they were dried in air at 100ºC for 24 hrs. Then, the samples were soaked in SBF for 1, 3 and 7 days. Fourier transformed infrared spectroscopy, thin-film X-ray diffraction, and scanning electron microscopy showed that after the calcium silicate treatment and the subsequent soaking in SBF, the microspheres successfully formed a bonelike apatite layer on their surfaces in SBF within 7 days due to the formation of silanol (Si-OH) groups that are quite effective for apatite formation.I. B. Leonor thanks the Portuguese Foundation for Science and Technology (FCT) for providing her a PhD scholarship (SFRH/BD/9031/2002) and the European Union funded STREP Project HIPPOCRATES (NMP3-CT-2003-505758) and the European NoE EXPERTISSUES (NMP3-CT-2004-500283)

Surface potential change in bioactive polymer during the process of biomimetic apatite formation in a simulated body fluid

A bioactive polyethylene substrate can be produced by incorporation of sulfonic functional groups (-SO3H) on its surface and by soaking in a calcium hydroxide saturated solution. Variation of the surface potential of the polyethylene modified with -SO3H groups with soaking in a simulated body fluid (SBF) was investigated using a laser electrophoresis zeta-potential analyzer. To complement the study using laser electrophoresis, the surface was examined by X-ray photoelectron spectroscopy (XPS), thin film X-ray diffraction (TF-XRD), field-emission scanning electron microscopy (FE-SEM) and energy-dispersive electron X-ray spectroscopy (EDS). Comparing the zeta potential of sulfonated and Ca(OH)2-treated polyethylene with its surface structure at each interval of these soaking times in SBF, it is apparent that the polymer has a negative surface potential when it forms -SO3H groups on its surface. The surface potential of the polymer increases when it forms amorphous calcium sulfate. The potential decreases when it forms amorphous calcium phosphate, revealing a constant negative value after forming apatite. The XPS and zeta potential analysis demonstrated that the surface potential of the polyethylene was highly negatively charged after soaking in SBF for 0.5 h, increased for higher soaking times (up to 48 h), and then decreased. The negative charge of the polymer at a soaking time of 0.5 h is attributed to the presence of -SO3H groups on the surface. The initial increase in the surface potential was attributed to the incorporation of positively charged calcium ions to form calcium sulfate, and then the subsequent decrease was assigned to the incorporation of negatively charged phosphate ions to form amorphous calcium phosphate, which eventually transformed into apatite. These results indicate that the formation of apatite on bioactive polyethylene in SBF is due to electrostatic interaction of the polymer surface and ions in the fluid

Formation of bone-like apatite on polymeric surfaces modified with -SO3H groups

Sulfonic groups (-SO3H) were covalently attached on different polymeric surfaces enabling them to induce apatite nucleation, for developing bioactive apatite-polymer composites with a bonelike 3-dimensional structure. High molecular weight polyethylene (HMWPE) and ethylene-co-vinyl alcohol co-polymer (EVOH) were used. The polymers were soaked in two types of sulphate-containing solutions with different concentrations, sulphuric acid (H2SO4) and chlorosulfonic acid (ClSO3H). To incorporate calcium ions into to the sulfonated polymers, the samples were soaked in a saturated Ca(OH)2 solution for 24 hours. After soaking of the samples in a simulated body fluid (SBF), formation of an apatite layer on both surfaces was observed. The results obtained prove the validity of the proposed concept and show that the -SO3H groups are effective on inducing apatite nucleation on the surface of these polymers.(undefined

Growth of a bonelike apatite on chitosan microparticles after a calcium silicate treatment

Bioactive chitosan microparticles can be prepared successfully by treating them with a calcium silicate solution and then subsequently soaking them in simulated body fluid (SBF). Such a combination enables the development of bioactive microparticles that can be used for several applications in the medical field, including injectable biomaterial systems and tissue engineering carrier systems. Chitosan microparticles, 0.6 lm in average size, were soaked either for 12 h in fresh calcium silicate solution (condition I) or for 1 h in calcium silicate solution that had been aged for 24 h before use (condition II). Afterwards, they were dried in air at 60 !C for 24 h. The samples were then soaked in SBF for 1, 3 and 7 days. After the condition I calcium silicate treatment and the subsequent soaking in SBF, the microparticles formed a dense apatite layer after only 7 days of immersion, which is believed to be due to the formation of silanol (Si– OH) groups effective for apatite formation. For condition II, the microparticles successfully formed an apatite layer on their surfaces in SBF within only 1 day of immersion.I.B.L. thanks the Portuguese Foundation for Science and Technology (FCT), for providing her a PhD scholarship (SFRH/BD/9031/2002), the European Union funded STREP Project HIPPOCRATES (NMP3-CT-2003-505758) and the European NoE EXPERTISSUES (NMP3-CT-2004-500283)

Electrical model of carbon fibre reinforced polymers for the development of electrical protection systems for more-electric aircraft

Carbon fibre reinforced polymers (CFRP) are increasingly used for structures on aircraft due to their superior mechanical properties compared to traditional materials, such as aluminium. Additionally, in order to improve aircraft performance, there is a continued trend for electrically driven loads on aircraft, increasing the on-board electrical power generation capacity and complexity of the electrical power system, including a desire to increase voltage levels and move towards DC distribution systems. Central to the reliable operation of an electrical power system is the development of an appropriate protection and fault management strategy. If an electrical earth fault occurs on a composite more-electric aircraft then the CFRP may form part of the route to ground. In order to develop an appropriate protection system and thus to understand the effects on engine generators it is necessary to investigate the fault response of this network. Hence a suitable electrical model of the CFRP material is required, which will enable CFRP to be included in a computationally-intensive systems-level simulation study of a more-electric aircraft (MEA) with fully switching power electronic converter models. This paper presents an experimentally validated impedance model of CFRP at an appropriate level of fidelity for use in systems level simulation platforms, enabling appropriate protection methods to be developed. The validated model considers the impact of the electrical bonding to ground, including the impedance added by a metallic frame that a CFRP panel may be mounted in. The simplicity of the model results in a less complex process to determine the expected impedance of the CFRP material, enabling a focus on the fault response of the system and subsequent development of appropriate protection solutions

An integrated numerical model for investigating guided waves in impact-damaged composite laminates

This paper presents a novel numerical technique that combines predictions of impact-induced damage and subsequent ultrasonic guided-wave propagation in composite laminates, with emphasis on the development and verification of the modelling framework. Delamination and matrix cracking are considered in the modelling technique, which is validated by experimental measurements on a carbon-fibre/epoxy plate using a drop-weight impact tower and a scanning laser vibrometer. Good agreement has been found between simulations and experiments regarding the impact response and global-local wavefields. Effects of these two damage modes, damage extent and multiple impacts on guided waves are studied using the modelling tool. Matrix cracking leads to lower wavefield scattering compared with delamination, particularly in un-damaged regions. The modelling strategy can provide valuable guidelines for optimising health-monitoring arrangements on composite structures that are susceptible to impacts, and the guided-wave model can also be integrated with other numerical models for predicting internal flaws in composite laminates

Delamination characteristics of glare laminates containing doubler and splice features under high cycle fatigue loading

A modified cohesive zone model (CZM) has been developed to simulate damage initiation and evolution inGlare™ Fibre-Metal Laminate (FML) specimens containing both splice and doubler features under high-cycle fatigue loading. The model computes the cohesive stiffness degradation under mixed-mode loading based on user-defined crack growth rate data and is implemented in a VUMAT subroutine for the FEA software Abaqus/Explicit. To validate the model experimental data has been obtained for a number of Glare 4B specimens containing splice and doubler features monitored using digital image correlation (DIC) to provide full-field displacement and strain data and Acoustic Emission (AE) monitoring to detect damage initiation and propagation. The model was used to predict the initiation and growth of damage in splice joints under quasi-static loading. The results were verified against the cohesive zone model available in Abaqus and then validated against experimental data on Glare specimens. The codes are currently being extended to incorporate a mixed-mode fatigue damage evolution model based on input Paris laws, which have been extracted from high cycle fatigue experiments on Glare specimens containing both splice and doubler joints