Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

Learning domain-specific sentiment lexicons for predicting product sales

Generic sentiment lexicons have been widely used for sentiment analysis these days. However, manually constructing sentiment lexicons is very time-consuming and it may not be feasible for certain application domains where annotation expertise is not available. One contribution of this paper is the development of a statistical learning based computational method for the automatic construction of domain-specific sentiment lexicons to enhance cross-domain sentiment analysis. Our initial experiments show that the proposed methodology can automatically generate domain-specific sentiment lexicons which contribute to improve the effectiveness of opinion retrieval at the document level. Another contribution of our work is that we show the feasibility of applying the sentiment metric derived based on the automatically constructed sentiment lexicons to predict product sales of certain product categories. Our research contributes to the development of more effective sentiment analysis system to extract business intelligence from numerous opinionated expressions posted to the Web

A method for measuring the creative potential of computer games

This paper describes a method for measuring the creative potential of computer games. The research approach applies a behavioral and verbal protocol to analyze the factors that influence the creative processes used by people as they play computer games from the puzzle genre. Creative potential is measured by examining task motivation and domain-relevant and creativity-relevant skills. This paper focuses on the reliability of the factors used for measurement, determining those factors that are more strongly related to creativity. The findings show that creative potential may be determined by examining the relationship between skills required and the effect of intrinsic motivation within game play activities.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Harmonic elimination technique for a single-phase multilevel converter with unequal DC link voltage levels

Multilevel converters, because of the benefits they attract in generating high quality output voltage, are used in several applications. Various modulation and control techniques are introduced by several researchers to control the output voltage of the multilevel converters like space vector modulation and harmonic elimination (HE) methods. Multilevel converters may have a DC link with equal or unequal DC voltages. In this study a new HE technique based on the HE method is proposed for multilevel converters with unequal DC link voltage. The DC link voltage levels are considered as additional variables for the HE method and the voltage levels are defined based on the HE results. Increasing the number of voltage levels can reduce lower order harmonic content because of the fact that more variables are created. In comparison to previous methods, this new technique has a positive effect on the output voltage quality by reducing its total harmonic distortion, which must take into consideration for some applications such as uninterruptable power supply, motor drive systems and piezoelectric transducer excitation. In order to verify the proposed modulation technique, MATLAB simulations and experimental tests are carried out for a single-phase four-level diode-clamped converter.

A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

An ontology-based method for sparsity problem in tag recommendation

Tags or personal metadata for annotating web resources have been widely adopted in Web 2.0 sites. However, as tags are freely chosen by users, the vocabularies are diverse, ambiguous and sometimes only meaningful to individuals. Tag recommenders may assist users during tagging process. Its objective is to suggest relevant tags to use as well as to help consolidating vocabulary in the systems. In this paper we discuss our approach for providing personalized tag recommendation by making use of existing domain ontology generated from folksonomy. Specifically we evaluated the approach in sparse situation. The evaluation shows that the proposed ontology-based method has improved the accuracy of tag recommendation in this situation.

A novel method for finding similarities between unordered trees using matrix data model

Trees are capable of portraying the semi-structured data which is common in web domain. Finding similarities between trees is mandatory for several applications that deal with semi-structured data. Existing similarity methods examine a pair of trees by comparing through nodes and paths of two trees, and find the similarity between them. However, these methods provide unfavorable results for unordered tree data and result in yielding NP-hard or MAX-SNP hard complexity. In this paper, we present a novel method that encodes a tree with an optimal traversing approach first, and then, utilizes it to model the tree with its equivalent matrix representation for finding similarity between unordered trees efficiently. Empirical analysis shows that the proposed method is able to achieve high accuracy even on the large data sets.

Identification and elimination of a matrix-induced systematic error in LA–ICP–MS 206Pb/238U dating of zircon

Black et al. (2004) identified a systematic difference between LA–ICP–MS and TIMS measurements of 206Pb/238U in zircons, which they correlated with the incompatible trace element content of the zircon. We show that the offset between the LA–ICP–MS and TIMS measured 206Pb/238U correlates more strongly with the total radiogenic Pb than with any incompatible trace element. This suggests that the cause of the 206Pb/238U offset is related to differences in the radiation damage (alpha dose) between the reference and unknowns. We test this hypothesis in two ways. First, we show that there is a strong correlation between the difference in the LA–ICP–MS and TIMS measured 206Pb/238U and the difference in the alpha dose received by unknown and reference zircons. The LA–ICP–MS ages for the zircons we have dated can be as much as 5.1% younger than their TIMS age to 2.1% older, depending on whether the unknown or reference received the higher alpha dose. Second, we show that by annealing both reference and unknown zircons at 850 °C for 48 h in air we can eliminate the alpha-dose-induced differences in measured 206Pb/238U. This was achieved by analyzing six reference zircons a minimum of 16 times in two round robin experiments: the first consisting of unannealed zircons and the second of annealed grains. The maximum offset between the LA–ICP–MS and TIMS measured 206Pb/238U for the unannealed zircons was 2.3%, which reduced to 0.5% for the annealed grains, as predicted by within-session precision based on counting statistics. Annealing unknown zircons and references to the same state prior to analysis holds the promise of reducing the 3% external error for the measurement of 206Pb/238U of zircon by LA–ICP–MS, indicated by Klötzli et al. (2009), to better than 1%, but more analyses of annealed zircons by other laboratories are required to evaluate the true potential of the annealing method.

Estimation of vibration amplitude in Fourier domain optical coherence tomography interferometric signals from Doppler spectrum

In presented method combination of Fourier and Time domain detection enables to broaden the effective bandwidth for time dependent Doppler Signal that allows for using higher-order Bessel functions to calculate unambiguously the vibration amplitudes.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Hybrid genetic algorithm for elimination of severe stress concentration in railhead ends

This paper presents a computational method for eliminating severe stress concentration at the unsupported railhead ends in rail joints through innovative shape optimization of the contact zone, which is complex due to near field nonlinear contact. With a view to minimizing the computational efforts, hybrid genetic algorithm method coupled with parametric finite element has been developed and compared with the traditional genetic algorithm (GA). The shape of railhead top surface where the wheel contacts nonlinearly was optimized using the hybridized GA method. Comparative study of the optimal result and the search efficiency between the traditional and hybrid GA methods has shown that the hybridized GA provides the optimal shape in fewer computational cycles without losing accuracy. The method will be beneficial to solving complex engineering problems involving contact nonlinearity.