Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials

This paper presents a computational approach for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method

Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations

We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence

Adaptive flexibility function in smart energy systems: A linearized price-demand mapping approach

This paper proposes an adaptive mechanism for price signal generation using a piecewise linear approximation of a flexibility function with unknown parameters. In this adaptive approach, the price signal is parameterized and the parameters are changed adaptively such that the output of the flexibility function follows the reference demand signal provided by the involved aggregator. This is guaranteed using the Lyapunov stability theorem. The proposed method does not require an estimation algorithm for unknown parameters, that eliminates the need for persistency of excitation of signals, and consequently, simplifies offering the flexibility services. Furthermore, boundedness of the price signal is ensured using a projection algorithm in the adaptive system. We present simulation results that demonstrate the price generation results using the proposed approaches

Comparative structural and mechanical studies on polyamide 6 knitted-reinforced single polymer composites prepared by different reactive processing techniques

Single polymer laminate composites based on anionic polyamide 6 (PA6) matrix-reinforced by PA6 knitted textile structures (KSPC) were produced by nylon reactive injection molding and powder coating/compression molding (PCCM) processing techniques. The effect of the reinforcement’s structure and the fiber volume fraction on the mechanical properties of the knitted-reinforced PA6 composites resulting from the two methods were investigated and compared. The morphology and the crystalline structure of KSPC materials were studied to identify the main factors determining the tensile properties. The results showed that the PCCM method produced laminate composites with higher Young’s modulus and mechanical strength in tension. Microscopy, differential scanning calorimetry and X-ray diffraction experiments were carried out to correlate the morphology and crystalline structure of the composites and their precursors with the different tensile behavior of KSPC prepared using the two techniques. The microscopy and X-ray scattering studies suggested the formation of a transcrystalline layer at the matrix/reinforcement interface. POLYM. COMPOS., 40:E886–E897, 2019. © 2018 Society of Plastics EngineersThis work was partially financed by FEDER funds through the COMPETE program and by national funds through FCT – Foundation for Science and Technology within the project POCI‐01‐0145‐FEDER‐007136. SDT thanks FCT for his PhD Grant SFRH/BD/94759/2013. NVD thanks for the financial support of FCT in the frames of the strategic project UID/CTM/50025/2013. Finally, ZZD is thankful to FCT for the SFRH/BSAB/130271/2017 personal research grant. All authors gratefully acknowledge the support of the project TSSiPRO‐NORTE‐01‐0145‐FEDER‐000015 funded by the regional operational program NORTE 2020, under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund

Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials

This paper presents a computational approach for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method

Mechano-morphological studies of polyamide 6 based single polymer laminate composites prepared by different reactive processing techniques

Single polymer laminate composites based on polyamide 6 (PA6) were prepared by two methods: (i) reactive injection molding and (ii) powder coating/compression molding, both carried out in the presence of PA6 woven textile plies. The effect of the textile volume fraction Vf on the tensile properties of all composites was investigated. The laminates obtained by powder coating/compression molding displayed best mechanical performance, whereby in the composites with Vf = 15%, the improvement of the elastic modulus reached 98% in respect to commercial hydrolytic PA6 reference, or 50–86% as compared to neat anionic PA6 samples. Polarizing light microscopy with image processing was used for morphological characterization. A transcrystalline layer at the fiber-matrix interface was detected in all laminates with thicknesses between 0.5 and 3.0 μm, depending on the preparation technique applied. The thermal stability was studied in the temperature range of 30°C-550 °C. The laminates obtained by reactive injection molding displayed the lowest initial decomposition temperature due to the presence of oligomers. Selected laminate composites were reprocessed by grinding and injection molding. The recycled composites obtained by powder coating displayed a 38% increase of the elastic modulus in respect to commercial hydrolytic PA6 thus confirming the sustainability and recyclability of PA6-based single polymer composites.This work was partially financed by FEDER funds through the COMPETE program and by national funds through FCT – Foundation for Science and Technology within the project .POCI-01-0145-FEDER 007136 SDT thanks FCT for his PhD Grant SFRH/BD/94759/2013. ZZD and NVD thank the National Funds through FCT-Portuguese Foundation for Science and Technology, project reference UID/CTM/50025/2019. All authors gratefully acknowledge the support of the project TSSiPRO NORTE-01-0145-FEDER-000015 funded by the regional operational program NORTE 2020, under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund

External review of the storage plan for the Peterhead Carbon Capture and Storage Project

This document summarises the findings of an external independent review of the storage plan for the proposed Peterhead Carbon Capture and Storage project which aims to store up to 20 million tonnes (Mt) of CO2 within the framework of the European Directive on the geological storage of CO2. The Peterhead Carbon Capture and Storage Project proposes to capture carbon dioxide (CO2) from an existing gas-fired power-station at Peterhead and to store this in geological strata at a depth of around 2600 m beneath the outer Moray Firth. The plan is to store 10 - 15 Mt of CO2 over a ten to fifteen-year period commencing around 2020, but the site is being qualified for 20 Mt to allow for potential extension of the injection period. Storage will utilise the depleted Goldeneye gas condensate field with the Captain Sandstone reservoir as the primary storage container. The Storage Site covers some 70 km2, and comprises the Captain Sandstone and underlying strata of the Cromer Knoll Group, bounded by a polygon some 2 to 3 km outside of the original Goldeneye oil-water contact. The Storage Complex is larger, around 154 km2, bounded some 2 to 7 km outside of the original oil-water contact, and extending upwards to the top of the Dornoch Mudstone at a depth of more than 800 m. The top-seal of the primary container is a proven caprock for natural gas and is formed by the mudstones of the Upper Cromer Knoll Group, the overlying Rødby and Hidra formations and the Plenus Marl. A number of additional seals are present in the overburden within the Storage Complex, as are a number of potential secondary containers which could also serve as monitoring horizons. The geological interpretation of the storage site is based on the comprehensive datasets acquired during the discovery, appraisal and development of the Goldeneye field, and also data from other wells, fields and seismic surveys in the surrounding area. The static geological model of the storage site and adjacent aquifer has been stress tested for the key uncertainties, and it is considered to be robust. The storage capacity of the Goldeneye structure has been calculated using both static (volumetric) methods and dynamic flow modelling together with uncertainty analysis. Total estimated capacity of the structural closure is in the range 25 to 47 Mt and so robustly exceeds the proposed injected amount

A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation

A new and efficient numerical approach is developed for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation. The fundamental structure of the presented method is based on the Tau method together with the Bernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Also, under several mild conditions the error analysis of the proposed method is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All calculations are done in Maple 13