An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

Evidence of multiwall carbon nanotube deformation caused by poly(3-hexylthiophene) adhesion

We show that when a soft polymer like Poly(3-hexyl-thiophene) wraps multiwall nanotubes by coiling around the main axis, a localized deformation of the nanotube structure is observed. High resolution transmission electron microscopy shows that radial compressions of about 4% can take place, and could possibly lead to larger interlayer distance between the nanotube inner walls and reduce the innermost nanotube radius. The mechanical stress due to the polymer presence was confirmed by Raman spectroscopic observation of a gradual upshift of the carbon nanotube G-band when the polymer content in the composites was progressively increased. Vibrational spectroscopy also indicates that charge transfer from the polymer to the nanotubes is responsible for a peak frequency relative downshift for high P3HT-content samples. Continuously acquired transmission electron microscopy images at rising temperature show the MWCNT elastic compression and relaxation due to polymer rearrangement on the nanotube surface.

Experimental study of the concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. The properties of the jet were examined far enough downstream to be relevant to the eventual modelling of the mixing problem. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm in a weak co-flow of 0.04 m/s. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller, which was placed in a glass-walled flume 0.4 m wide with a free surface depth of 0.15 m. The jet and scalar plume development were compared to that of a classical free round jet. Further, results pertaining to radial distribution, self similarity, standard deviation growth, maximum value decay and integral fluxes of velocity and concentration were presented and fitted with empirical correlations. Furthermore, propeller induced mixing and pollutant source concentration from a two-stroke engine were estimated.

Protection of distributed generation interfaced networks

With the rapid increase in electrical energy demand, power generation in the form of distributed generation is becoming more important. However, the connections of distributed generators (DGs) to a distribution network or a microgrid can create several protection issues. The protection of these networks using protective devices based only on current is a challenging task due to the change in fault current levels and fault current direction. The isolation of a faulted segment from such networks will be difficult if converter interfaced DGs are connected as these DGs limit their output currents during the fault. Furthermore, if DG sources are intermittent, the current sensing protective relays are difficult to set since fault current changes with time depending on the availability of DG sources. The system restoration after a fault occurs is also a challenging protection issue in a converter interfaced DG connected distribution network or a microgrid. Usually, all the DGs will be disconnected immediately after a fault in the network. The safety of personnel and equipment of the distribution network, reclosing with DGs and arc extinction are the major reasons for these DG disconnections. In this thesis, an inverse time admittance (ITA) relay is proposed to protect a distribution network or a microgrid which has several converter interfaced DG connections. The ITA relay is capable of detecting faults and isolating a faulted segment from the network, allowing unfaulted segments to operate either in grid connected or islanded mode operations. The relay does not make the tripping decision based on only the fault current. It also uses the voltage at the relay location. Therefore, the ITA relay can be used effectively in a DG connected network in which fault current level is low or fault current level changes with time. Different case studies are considered to evaluate the performance of the ITA relays in comparison to some of the existing protection schemes. The relay performance is evaluated in different types of distribution networks: radial, the IEEE 34 node test feeder and a mesh network. The results are validated through PSCAD simulations and MATLAB calculations. Several experimental tests are carried out to validate the numerical results in a laboratory test feeder by implementing the ITA relay in LabVIEW. Furthermore, a novel control strategy based on fold back current control is proposed for a converter interfaced DG to overcome the problems associated with the system restoration. The control strategy enables the self extinction of arc if the fault is a temporary arc fault. This also helps in self system restoration if DG capacity is sufficient to supply the load. The coordination with reclosers without disconnecting the DGs from the network is discussed. This results in increased reliability in the network by reduction of customer outages.

Prediction of cis/trans isomerization in proteins using PSI-BLAST profiles and secondary structure information

Background The majority of peptide bonds in proteins are found to occur in the trans conformation. However, for proline residues, a considerable fraction of Prolyl peptide bonds adopt the cis form. Proline cis/trans isomerization is known to play a critical role in protein folding, splicing, cell signaling and transmembrane active transport. Accurate prediction of proline cis/trans isomerization in proteins would have many important applications towards the understanding of protein structure and function. Results In this paper, we propose a new approach to predict the proline cis/trans isomerization in proteins using support vector machine (SVM). The preliminary results indicated that using Radial Basis Function (RBF) kernels could lead to better prediction performance than that of polynomial and linear kernel functions. We used single sequence information of different local window sizes, amino acid compositions of different local sequences, multiple sequence alignment obtained from PSI-BLAST and the secondary structure information predicted by PSIPRED. We explored these different sequence encoding schemes in order to investigate their effects on the prediction performance. The training and testing of this approach was performed on a newly enlarged dataset of 2424 non-homologous proteins determined by X-Ray diffraction method using 5-fold cross-validation. Selecting the window size 11 provided the best performance for determining the proline cis/trans isomerization based on the single amino acid sequence. It was found that using multiple sequence alignments in the form of PSI-BLAST profiles could significantly improve the prediction performance, the prediction accuracy increased from 62.8% with single sequence to 69.8% and Matthews Correlation Coefficient (MCC) improved from 0.26 with single local sequence to 0.40. Furthermore, if coupled with the predicted secondary structure information by PSIPRED, our method yielded a prediction accuracy of 71.5% and MCC of 0.43, 9% and 0.17 higher than the accuracy achieved based on the singe sequence information, respectively. Conclusion A new method has been developed to predict the proline cis/trans isomerization in proteins based on support vector machine, which used the single amino acid sequence with different local window sizes, the amino acid compositions of local sequence flanking centered proline residues, the position-specific scoring matrices (PSSMs) extracted by PSI-BLAST and the predicted secondary structures generated by PSIPRED. The successful application of SVM approach in this study reinforced that SVM is a powerful tool in predicting proline cis/trans isomerization in proteins and biological sequence analysis.

Pattern recognition using invariants defined from higher order spectra : 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Distribution feeder voltage support and power factor control by distributed multiple inverters

The potential of distributed reactive power control to improve the voltage profile of radial distribution feeders has been reported in literature by few authors. However, the multiple inverters injecting or absorbing reactive power across a distribution feeder may introduce control interactions and/or voltage instability. Such controller interactions can be alleviated if the inverters are allowed to operate on voltage droop. First, the paper demonstrates that a linear shallow droop line can maintain the steady state voltage profile close to reference, up to a certain level of loading. Then, impacts of the shallow droop line control on line losses and line power factors are examined. Finally, a piecewise linear droop line which can achieve reduced line losses and close to unity power factor at the feeder source is proposed.

Distributed DSTATCOMs for distribution line enhancement

Distribution feeder voltage reinforcement by multiple site reactive power compensation systems has recently been reported by many researchers. However, voltage control by multiple DSTATCOMs across a distribution feeder may introduce control interactions and/or voltage instability. This paper addresses these control interaction issues and proposes a control scheme that alleviates interactions among controllers. The proposed control scheme also enhances proper sharing of reactive power among DSTATCOMs. A mathematical model of a distribution system with any number of DSTATCOMs is developed to investigate the performance of the control system. This mathematical model is used to conduct eigenvalue analysis to develop the criterion for controller design. The proposed control scheme is tested in time domain on a sample radial distribution feeder installed with multiple DSTATCOMs and test results are presented.

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

CgDN24 : a gene involved in hyphal development in the fungal phytopathogen Colletotrichum gloeosporioides

A cDNA corresponding to a transcript induced in culture by N starvation, was identified in Colletotrichum gloeosporioides by a differential hybridisation strategy. The cDNA comprised 905 bp and predicted a 215 aa protein; the gene encoding the cDNA was termed CgDN24. No function for CgDN24 could be predicted by database homology searches using the cDNA sequence and no homologues were found in the sequenced fungal genomes. Transcripts of CgDN24 were detected in infected leaves of Stylosanthes guianensis at stages of infection that corresponded with symptom development. The CgDN24 gene was disrupted by homologous recombination and this led to reduced radial growth rates and the production of hyphae with a hyperbranching phenotype. Normal sporulation was observed, and following conidial inoculation of S. guianensis, normal disease development was obtained. These results demonstrate that CgDN24 is necessary for normal hyphal development in axenic culture but dispensable for phytopathogenicity. © 2005 Elsevier GmbH. All rights reserved.

Analysis of electromagnetic forces in high voltage superconducting fault current limiters with saturated core

This paper presents a three-dimensional numerical analysis of the electromagnetic forces within a high voltage superconducting Fault Current Limiter (FCL) with a saturated core under short-circuit conditions. The effects of electrodynamics forces in power transformer coils under short-circuit conditions have been reported widely. However, the coil arrangement in an FCL with saturated core differs significantly from existing reactive devices. The boundary element method is employed to perform an electromagnetic force analysis on an FCL. The analysis focuses on axial and radial forces of the AC coil. The results are compared to those of a power transformer and important design considerations are highlighted.

Analysis of conical-cylinder shells fundamental characteristics for structural health diagnostics

This paper describes the formulation for the free vibration of joined conical-cylindrical shells with uniform thickness using the transfer of influence coefficient for identification of structural characteristics. These characteristics are importance for structural health monitoring to develop model. This method was developed based on successive transmission of dynamic influence coefficients, which were defined as the relationships between the displacement and the force vectors at arbitrary nodal circles of the system. The two edges of the shell having arbitrary boundary conditions are supported by several elastic springs with meridional/axial, circumferential, radial and rotational stiffness, respectively. The governing equations of vibration of a conical shell, including a cylindrical shell, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-cylindrical shells. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of previous researchers.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.