A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Sertraline accumulation and effects in the estuarine decapod Carcinusmaenas: Importance of the history of exposure to chemical stress

Sertraline is widely prescribed worldwide and frequently detected in aquatic systems. There is, however, a remarkable gap of information on its potential impact on estuarine and coastal invertebrates. This study investigated sertraline accumulation and effects in Carcinus maenas. Crabs from a moderately contaminated (Lima) and a low-impacted (Minho) estuary were exposed to environmental and high levels of sertraline (0.05, 5, 500 μg L−1). A battery of biomarkers related to sertraline mode of action was employed to assess neurotransmission, energy metabolism, biotransformation and oxidative stress pathways. After a seven-day exposure, sertraline accumulation in crabs’ soft tissues was found in Lima (5 μg L−1: 15.3 ng L−1 ww; 500 μg L−1: 1010 ng L−1 ww) and Minho (500 μg L−1: 605 ng L−1 ww) animals. Lima crabs were also more sensitive to sertraline than those from Minho, exhibiting decreased acetylcholinesterase activity, indicative of ventilatory and locomotory dysfunction, inhibition of anti-oxidant enzymes and increased oxidative damage at ≥0.05 μg L−1. The Integrated Biomarker Response (IBR) index indicated their low health status. In addition, Minho crabs showed non-monotonic responses of acetylcholinesterase suggestive of hormesis. The results pointed an influence of the exposure history on differential sensitivity to sertraline and the need to perform evaluations with site-specific ecological receptors to increase relevance of risk estimations when extrapolating from laboratory to field conditions.

Isoflavones in food supplements: chemical profile, label accordance and permeability study in Caco-2 cells

Consumers nowadays are playing an active role in their health-care. A special case is the increasing number of women, who are reluctant to use exogenous hormone therapy for the treatment of menopausal symptoms and are looking for complementary therapies. However, food supplements are not clearly regulated in Europe. The EFSA has only recently begun to address the issues of botanical safety and purity regulation, leading to a variability of content, standardization, dosage, and purity of available products. In this study, isoflavones (puerarin, daidzin, genistin, daidzein, glycitein, genistein, formononetin, prunetin, and biochanin A) from food supplements (n = 15) for menopausal symptoms relief are evaluated and compared with the labelled information. Only four supplements complied with the recommendations made by the EC on the tolerable thresholds. The intestinal bioavailability of these compounds was investigated using Caco-2 cells. The apparent permeability coefficients of the selected isoflavonoids across the Caco-2 cells were affected by the isoflavone concentration and product matrix.

Fire effects on soil after an experimental burnt

5th International Conference of Fire Effects on Soil Properties

Adhesive selection for single lap bonded joints: Experimentation and advanced techniques for strength prediction

The integrity of multi-component structures is usually determined by their unions. Adhesive-bonding is often used over traditional methods because of the reduction of stress concentrations, reduced weight penalty, and easy manufacturing. Commercial adhesives range from strong and brittle (e.g., Araldite® AV138) to less strong and ductile (e.g., Araldite® 2015). A new family of polyurethane adhesives combines high strength and ductility (e.g., Sikaforce® 7888). In this work, the performance of the three above-mentioned adhesives was tested in single lap joints with varying values of overlap length (LO). The experimental work carried out is accompanied by a detailed numerical analysis by finite elements, either based on cohesive zone models (CZM) or the extended finite element method (XFEM). This procedure enabled detailing the performance of these predictive techniques applied to bonded joints. Moreover, it was possible to evaluate which family of adhesives is more suited for each joint geometry. CZM revealed to be highly accurate, except for largely ductile adhesives, although this could be circumvented with a different cohesive law. XFEM is not the most suited technique for mixed-mode damage growth, but a rough prediction was achieved.

Adhesive thickness effects of a ductile adhesive by optical measurement techniques

Adhesive bonding is an excellent alternative to traditional joining techniques such as welding, mechanical fastening or riveting. However, there are many factors that have to be accounted for during joint design to accurately predict the joint strength. One of these is the adhesive layer thickness (tA). Most of the results are for epoxy structural adhesives, tailored to perform best with small values of tA, and these show that the lap joint strength decreases with increase of tA (the optimum joint strength is usually obtained with tA values between 0.1 and 0.2 mm). Recently, polyurethane adhesives were made available in the market, designed to perform with larger tA values, and whose fracture behaviour is still not studied. In this work, the effect of tA on the tensile fracture toughness (View the MathML source) of a bonded joint is studied, considering a novel high strength and ductile polyurethane adhesive for the automotive industry. This work consists on the fracture characterization of the bond by a conventional and the J-integral techniques, which accurately account for root rotation effects. An optical measurement method is used for the evaluation of crack tip opening (δn) and adherends rotation at the crack tip (θo) during the test, supported by a Matlab® sub-routine for the automated extraction of these parameters. As output of this work, fracture data is provided in traction for the selected adhesive, enabling the subsequent strength prediction of bonded joints.

Tensile fracture characterization of adhesive joints by standard and optical techniques

The use of adhesive joints has increased in recent decades due to its competitive features compared with traditional methods. This work aims to estimate the tensile critical strain energy release rate (GIC) of adhesive joints by the Double-Cantilever Beam (DCB) test. The J-integral is used since it enables obtaining the tensile Cohesive Zone Model (CZM) law. An optical measuring method was developed for assessing the crack tip opening (δn) and adherends rotation (θo). The proposed CZM laws were best approximated by a triangular shape for the brittle adhesive and a trapezoidal shape for the two ductile adhesives.

Effects of self-administered exercises based on Tuina techniques on musculoskeletal disorders of professional orchestra musicians: a randomized controlled trial

Background Musicians are frequently affected by playing-related musculoskeletal disorders (PRMD). Common solutions used by Western medicine to treat musculoskeletal pain include rehabilitation programs and drugs, but their results are sometimes disappointing. Objective To study the effects of self-administered exercises based on Tuina techniques on the pain intensity caused by PRMD of professional orchestra musicians, using numeric visual scale (NVS). Design, setting, participants and interventions We performed a prospective, controlled, single-blinded, randomized study with musicians suffering from PRMD. Participating musicians were randomly distributed into the experimental (n = 39) and the control (n = 30) groups. After an individual diagnostic assessment, specific Tuina self-administered exercises were developed and taught to the participants. Musicians were instructed to repeat the exercises every day for 3 weeks. Main outcome measures Pain intensity was measured by NVS before the intervention and after 1, 3, 5, 10, 15 and 20 d of treatment. The procedure was the same for the control group, however the Tuina exercises were executed in points away from the commonly-used acupuncture points. Results In the treatment group, but not the control group, pain intensity was significantly reduced on days 1, 3, 5, 10, 15 and 20. Conclusion The results obtained are consistent with the hypothesis that self-administered exercises based on Tuina techniques could help professional musicians controlling the pain caused by PRMD. Although our results are very promising, further studies are needed employing a larger sample size and double blinding designs.

Immediate effects of Tuina techniques on working-related musculoskeletal disorder of professional orchestra musicians

BACKGROUND: Musicians are a prone group to suffer from working-related musculoskeletal disorder (WRMD). Conventional solutions to control musculoskeletal pain include pharmacological treatment and rehabilitation programs but their efficiency is sometimes disappointing. OBJECTIVE: The aim of this research is to study the immediate effects of Tuina techniques on WRMD of professional orchestra musicians from the north of Portugal. DESIGN, SETTING, PARTICIPANTS AND INTERVENTIONS: We performed a prospective, controlled, single-blinded, randomized study. Professional orchestra musicians with a diagnosis of WRMD were randomly distributed into the experimental group (n=39) and the control group (n=30). During an individual interview, Chinese diagnosis took place and treatment points were chosen. Real acupoints were treated by Tuina techniques into the experimental group and non-specific skin points were treated into the control group. Pain was measured by verbal numerical scale before and immediately after intervention. RESULTS: After one treatment session, pain was reduced in 91.8% of the cases for the experimental group and 7.9% for the control group. CONCLUSION: Although results showed that Tuina techniques are effectively reducing WRMD in professional orchestra musicians of the north of Portugal, further investigations with stronger measurements, double-blinding designs and bigger simple sizes are needed.

Efficiency of strengthening techniques assessed for existing masonry buildings

The Azores archipelago is a zone with a vast cultural heritage, presenting a building stock mainly constructed in traditional stone masonry. It is known that this type of construction exhibits poor behaviour under seismic excitations; however it is extensively used in seismic prone areas, such as this case. The 9th of July of 1998 earthquake was the last seismic event in the islands, leaving many traditional stone constructions severely damaged or totally destroyed. This scenario led to an effort by the local government of improving the seismic resistance of these constructions, with the application of several reinforcement techniques. This work aims to study some of the most used reinforcement schemes after the 1998 earthquake, and to assess their effectiveness in the mitigation of the construction’s seismic vulnerability. A brief evaluation of the cost versus benefit of these retrofitting techniques is also made, seeking to identify those that are most suitable for each building typology. Thus, it was sought to analyze the case of real structures with different geometrical and physical characteristics, by establishing a comparison between the seismic performance of reinforced and non-reinforced structures. The first section contains the analysis of a total of six reinforcement scenarios for each building chosen. Using the recorded 1998 earthquake accelerograms, a linear time-history analysis was performed for each reinforcement scenario. A comparison was then established between the maximum displacements, inter-storey drift and maximum stress obtained, in order to evaluate the global seismic response of each reinforced structure. In the second part of the work, the examination of the performance obtained in the previous section, in relation to the cost of implementing each reinforcement technique, allowed to draw conclusions concerning the viability of implementing each reinforcement method, based on the book value of the buildings in study.