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.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

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.

Monte Carlo evaluation of collapsed-cone convolution calculations in head and neck radiotherapy treatment plans

The presence of air and bone interfaces makes the dose distribution for head and neck cancer treatments difficult to accurately predict. This study compared planning system dose calculations using the collapsed-cone convolution algorithm with EGSnrcMonte Carlo simulation results obtained using the Monte Carlo DICOMToolKit software, for one oropharynx, two paranasal sinus and three nodal treatment plans. The difference between median doses obtained from the treatment planning and Monte Carlo calculations was found to be greatest in two bilateral treatments: 4.8%for a retropharyngeal node irradiation and 6.7% for an ethmoid paranasal sinus treatment. These deviations in median dose were smaller for two unilateral treatments: 0.8% for an infraclavicular node irradiation and 2.8% for a cervical node treatment. Examination of isodose distributions indicated that the largest deviations between Monte Carlo simulation and collapsed-cone convolution calculations were seen in the bilateral treatments, where the increase in calculated dose beyond air cavities was most significant.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Accuracy of FEM and BEM for electromagnetic flux calculations in high power applications

The development and design of electric high power devices with electromagnetic computer-aided engineering (EM-CAE) software such as the Finite Element Method (FEM) and Boundary Element Method (BEM) has been widely adopted. This paper presents the analysis of a Fault Current Limiter (FCL), which acts as a high-voltage surge protector for power grids. A prototype FCL was built. The magnetic flux in the core and the resulting electromagnetic forces in the winding of the FCL were analyzed using both FEM and BEM. An experiment on the prototype was conducted in a laboratory. The data obtained from the experiment is compared to the numerical solutions to determine the suitability and accuracy of the two methods.

Oblique-Shock-Wave/Boundary-Layer Interaction Using Near-Wall Reynolds-Stress Models

A synthesis is presented of the predictive capability of a family of near-wall wall-normal free Reynolds stress models (which are completely independent of wall topology, i.e., of the distance fromthe wall and the normal-to-thewall orientation) for oblique-shock-wave/turbulent-boundary-layer interactions. For the purpose of comparison, results are also presented using a standard low turbulence Reynolds number k–ε closure and a Reynolds stress model that uses geometric wall normals and wall distances. Studied shock-wave Mach numbers are in the range MSW = 2.85–2.9 and incoming boundary-layer-thickness Reynolds numbers are in the range Reδ0 = 1–2×106. Computations were carefully checked for grid convergence. Comparison with measurements shows satisfactory agreement, improving on results obtained using a k–ε model, and highlights the relative importance of redistribution and diffusion closures, indicating directions for future modeling work.

Influence of inflow turbulence in shock-wave/turbulent-boundary-layer interaction computations

The influence of inflow turbulence on the results of Favre–Reynolds-averaged Navier–Stokes computations of supersonic oblique-shock-wave/turbulent-boundary-layer interactions (shock-wave Mach-number MSW ∼2.9), using seven-equation Reynolds-stress model turbulence closures, is studied. The generation of inflow conditions (and the initialization of the flowfield) for mean flow, Reynolds stresses, and turbulence length scale, based on semi-analytic grid-independent boundary-layer profiles, is described in detail. Particular emphasis is given to freestream turbulence intensity and length scale. The influence of external-flow turbulence intensity is studied in detail both for flat-plate boundary-layer flow and for a compression-ramp interaction with large separation. It is concluded that the Reynolds-stress model correctly reproduces the effects of external flow turbulence.

2nd Australian producer survey 2012 : understanding Australian screen content producers : wave 2

This report presents the top-line findings of the Australian Screen Producer survey conducted in December 2011. The report was prepared by Bergent Research and commissioned by the ARC Centre of Excellence for Creative Industries and Innovation (CCI), Queensland University of Technology, with assistance from the Centre for Screen Business, Australian Film Television and Radio School (AFTRS). The 2011 producer survey was a national study of the demographics, motivations, sentiments and activities of screen producers across four industry segments: Film, Television, Commercial and Digital Media. This survey is the second Australian Screen Producer survey and builds upon research undertaken in the Australian Screen Content Producer Survey conducted in 2009. The 2011 study is referred to in this report as Wave 2 and the 2009 study is referred to as Wave 1.

The development of a Monte Carlo system to verify radiotherapy treatment dose calculations

Recent advances in the planning and delivery of radiotherapy treatments have resulted in improvements in the accuracy and precision with which therapeutic radiation can be administered. As the complexity of the treatments increases it becomes more difficult to predict the dose distribution in the patient accurately. Monte Carlo methods have the potential to improve the accuracy of the dose calculations and are increasingly being recognised as the “gold standard” for predicting dose deposition in the patient. In this study, software has been developed that enables the transfer of treatment plan information from the treatment planning system to a Monte Carlo dose calculation engine. A database of commissioned linear accelerator models (Elekta Precise and Varian 2100CD at various energies) has been developed using the EGSnrc/BEAMnrc Monte Carlo suite. Planned beam descriptions and CT images can be exported from the treatment planning system using the DICOM framework. The information in these files is combined with an appropriate linear accelerator model to allow the accurate calculation of the radiation field incident on a modelled patient geometry. The Monte Carlo dose calculation results are combined according to the monitor units specified in the exported plan. The result is a 3D dose distribution that could be used to verify treatment planning system calculations. The software, MCDTK (Monte Carlo Dicom ToolKit), has been developed in the Java programming language and produces BEAMnrc and DOSXYZnrc input files, ready for submission on a high-performance computing cluster. The code has been tested with the Eclipse (Varian Medical Systems), Oncentra MasterPlan (Nucletron B.V.) and Pinnacle3 (Philips Medical Systems) planning systems. In this study the software was validated against measurements in homogenous and heterogeneous phantoms. Monte Carlo models are commissioned through comparison with quality assurance measurements made using a large square field incident on a homogenous volume of water. This study aims to provide a valuable confirmation that Monte Carlo calculations match experimental measurements for complex fields and heterogeneous media.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Hybrid graphene and graphitic carbon nitride nanocomposite : gap opening, electron–hole puddle, interfacial charge transfer, and enhanced visible light response

Opening up a band gap and finding a suitable substrate material are two big challenges for building graphene-based nanodevices. Using state-of-the-art hybrid density functional theory incorporating long range dispersion corrections, we investigate the interface between optically active graphitic carbon nitride (g-C3N4) and electronically active graphene. We find an inhomogeneous planar substrate (g-C3N4) promotes electronrich and hole-rich regions, i.e., forming a well-defined electron−hole puddle, on the supported graphene layer. The composite displays significant charge transfer from graphene to the g-C3N4 substrate, which alters the electronic properties of both components. In particular, the strong electronic coupling at the graphene/g-C3N4 interface opens a 70 meV gap in g-C3N4-supported graphene, a feature that can potentially allow overcoming the graphene’s band gap hurdle in constructing field effect transistors. Additionally, the 2-D planar structure of g-C3N4 is free of dangling bonds, providing an ideal substrate for graphene to sit on. Furthermore, when compared to a pure g-C3N4 monolayer, the hybrid graphene/g-C3N4 complex displays an enhanced optical absorption in the visible region, a promising feature for novel photovoltaic and photocatalytic applications.

C-BN Single-Walled Nanotubes from Hybrid Connection of BN/C Nanoribbons: Prediction by ab initio Density Functional Calculations

We demonstrated for the first time by ab initio density functional calculation and molecular dynamics simulation that C0.5(BN)0.5 armchair single-walled nanotubes (NT) are gapless semiconductors and can be spontaneously formed via the hybrid connection of graphene/BN Nanoribbons (GNR/BNNR) at room temperature. The direct synthesis of armchair C0.5(BN)0.5 via the hybrid connection of GNR/BNNR is predicted to be both thermodynamically and dynamically stable. Such novel armchair C0.5(BN)0.5 NTs possess enhanced conductance as that observed in GNRs. Additionally, the zigzag C0.5(BN)0.5 SWNTs are narrow band gap semiconductors, which may have potential application for light emission. In light of recent experimental progress and the enhanced degree of control in the synthesis of GNRs and BNNR, our results highlight an interesting avenue for synthesizing a novel specific type of C0.5(BN)0.5 nanotube (gapless or narrow direct gap semiconductor), with potentially important applications in BNC-based nanodevices.

Multifunctional porous graphene for nanoelectronics and hydrogen storage : new properties revealed by first principle calculations

The lack of an obvious “band gap” is a formidable hurdle for making a nanotransistor from graphene. Here, we use density functional calculations to demonstrate for the first time that porosity such as evidenced in recently synthesized porous graphene (http://www.sciencedaily.com/releases/2009/11/091120084337.htm) opens a band gap. The size of the band gap (3.2 eV) is comparable to most popular photocatalytic titania and graphitic C3N4 materials. In addition, the adsorption of hydrogen on Li-decorated porous graphene is much stronger than that in regular Li-doped graphene due to the natural separation of Li cations, leading to a potential hydrogen storage gravimetric capacity of 12 wt %. In light of the most recent experimental progress on controlled synthesis, these results uncover new potential for the practical application of porous graphene in nanoelectronics and clean energy.