Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

Modelling of the evaporation of a droplet suspended in a binary atmosphere

The process of spray drying is applied in a number of contexts. One such application is the production of a synthetic rock used for storage of nuclear waste. To establish a framework for a model of the spray drying process for this application, we here develop a model describing evaporation from droplets of pure water, such that the model may be extended to account for the presence of colloid within the droplet. We develop a spherically-symmetric model and formulate continuum equations describing mass, momentum, and energy balance in both the liquid and gas phases from first principles. We establish appropriate boundary conditions at the surface of the droplet, including a generalised Clapeyron equation that accurately describes the temperature at the surface of the droplet. To account for experiment design, we introduce a simplified platinum ball and wire model into the system using a thin wire problem. The resulting system of equations is transformed in order to simplify a finite volume solution scheme. The results from numerical simulation are compared with data collected for validation, and the sensitivity of the model to variations in key parameters, and to the use of Clausius–Clapeyron and generalised Clapeyron equations, is investigated. Good agreement is found between the model and experimental data, despite the simplicity of the platinum phase model.

A framing analysis on Nepalese media portrayal of disaster events using news frames and PPRR cycle

This study seeks to understand the prevailing status of Nepalese media portrayal of natural disasters and develop a disaster management framework to improve the effectiveness and efficiency of news production through the continuum of prevention, preparedness, response and recovery (PPRR) phases of disaster management. The study is currently under progress. It is being undertaken in three phases. In phase-1, a qualitative content analysis is conducted. The news contents are categorized in frames as proposed in the 'Framing theory' and pre-defined frames. However, researcher has looked at the theories of the Press, linking to social responsibility theory as it is regarded as the major obligation of the media towards the society. Thereafter, the contents are categorized as per PPRR cycle. In Phase-2, based on the findings of content analysis, 12 in-depth interviews with journalists, disaster managers and community leaders are conducted. In phase-3, based on the findings of content analysis and in-depth interviews, a framework for effective media management of disaster are developed using thematic analysis. As the study is currently under progress hence, findings from the pilot study are elucidated. The response phase of disasters is most commonly reported in Nepal. There is relatively low coverage of preparedness and prevention. Furthermore, the responsibility frame in the news is most prevalent following human interest. Economic consequences and conflict frames are also used while reporting and vulnerability assessment has been used as an additional frame. The outcomes of this study are multifaceted: At the micro-level people will be benefited as it will enable a reduction in the loss of human lives and property through effective dissemination of information in news and other mode of media. They will be ‘well prepared for', 'able to prevent', 'respond to' and 'recover from' any natural disasters. At the meso level the media industry will be benefited and have their own 'disaster management model of news production' as an effective disaster reporting tool which will improve in media's editorial judgment and priority. At the macro-level it will assist government and other agencies to develop appropriate policies and strategies for better management of natural disasters.

From the genius of man to the man of genius, part one: A slippery subject

The two articles that comprise this analysis springboard from the availability and increased popularity of the term genius to nineteenth and twentieth century educational scholars and its (temporary) location along a continuum of mindedness that was relatively new (i.e., as opposite to insanity). Three generations of analysis playfully structure the argument, taking form around the gen‐ root’s historical association with tropes of production and reproduction. Of particular interest in the analysis is how subject‐formation, including perceptions of non‐formation and elusivity, occurs. I examine this process of (non)formation within and across key texts on genius, especially in relation to their narrative structures, key binaries and sources of authority that collectively produce and embed specific cosmologies and their moral boundaries. The argument is staged across two articles that embody the three generations of analysis.

Dinner aesthetic

‘Dinner Aesthetic’ fictionally explores the theme of creation and destruction as points on a continuum, rather than oppositional binaries. The piece was published in in Issue 21 of Literary Orphans.

Instabilities and Waves in Thin Films of Living Fluids

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity, and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys. Fluids 13 1160 (2001)] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.

Exploring university-community partnerships in arts-based service learning with Australian First Peoples and Arts Organizations

In this chapter we focus on the importance of partnerships in arts-based service learning with Australian First Peoples and community arts organizations. Drawing on six years of our own partnership and a wide body of literature, this chapter aims to act as a trigger for further reflection on ways to engage in meaningful partnerships with First Peoples and arts organizations. In particular, the continuum between transactional and transformational types of relationships provides a useful means for understanding our work and for positioning the various benefits and challenges associated with university-community partnerships more broadly.

Wave propagation in multi-walled carbon nanotube

In this paper, wave propagation in multi-walled carbon nanotubes (MWNTs) are studied by modeling them as continuum multiple shell coupled through van der Waals force of interaction. The displacements, namely, axial, radial and circumferential displacements vary along the circumferential direction. The wave propagation are simulated using the wavelet based spectral finite element (WSFE) method. This technique involves Daubechies scaling function approximation in time and spectral element approach. The WSFE Method allows the study of wave properties in both time and frequency domains. This is in contrast to the conventional Fourier transform based analysis which are restricted to frequency domain analysis. Here, first, the wavenumbers and wave speeds of carbon nanotubes (CNTs) are Studied to obtain the characteristics of the waves. These group speeds have been compared with those reported in literature. Next, the natural frequencies of a single-walled carbon nanotube (SWNT) are studied for different values of the radius. The frequencies of the first five modes vary linearly with the radius of the SWNT. Finally, the time domain responses are simulated for SWNT and three-walled carbon nanotubes.

3D numerical simulation of avascular tumour growth: effect of hypoxic micro-environment in host tissue

A three-dimensional (3D) mathematical model of tumour growth at the avascular phase and vessel remodelling in host tissues is proposed with emphasis on the study of the interactions of tumour growth and hypoxic micro-environment in host tissues. The hybrid based model includes the continuum part, such as the distributions of oxygen and vascular endothelial growth factors (VEGFs), and the discrete part of tumour cells (TCs) and blood vessel networks. The simulation shows the dynamic process of avascular tumour growth from a few initial cells to an equilibrium state with varied vessel networks. After a phase of rapidly increasing numbers of the TCs, more and more host vessels collapse due to the stress caused by the growing tumour. In addition, the consumption of oxygen expands with the enlarged tumour region. The study also discusses the effects of certain factors on tumour growth, including the density and configuration of preexisting vessel networks and the blood oxygen content. The model enables us to examine the relationship between early tumour growth and hypoxic micro-environment in host tissues, which can be useful for further applications, such as tumour metastasis and the initialization of tumour angiogenesis.

Instability of laminated composite thin-walled open-section beams

Instability of thin-walled open-section laminated composite beams is studied using the finite element method. A two-noded, 8 df per node thin-walled open-section laminated composite beam finite element has been used. The displacements of the element reference axis are expressed in terms of one-dimensional first order Hermite interpolation polynomials, and line member assumptions are invoked in formulation of the elastic stiffness matrix and geometric stiffness matrix. The nonlinear expressions for the strains occurring in thin-walled open-section beams, when subjected to axial, flexural and torsional loads, are incorporated in a general instability analysis. Several problems for which continuum solutions (exact/approximate) are possible have been solved in order to evaluate the performance of finite element. Next its applicability is demonstrated by predicting the buckling loads for the following problems of laminated composites: (i) two layer (45°/−45°) composite Z section cantilever beam and (ii) three layer (0°/45°/0°) composite Z section cantilever beam.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

A technique for steady-state polarisation of stationary solid electrodes and its applications

A new technique has been devised to achieve a steady-state polarisation of a stationary electrode with a helical shaft rotating coaxial to it. A simplified theory for the convective hydrodynamics prevalent under these conditions has been formulated. Experimental data are presented to verify the steady-state character of the current-potential curves and the predicted dependence of the limiting current on the rotation speed of the rotor, the bulk concentration of the depolariser and the viscosity of the solution. Promising features of the multiple-segment electrodes concentric to a central disc electrode are pointed out.

Use of narrow-pore filters in He II transfer devices - new results

With the aim of finding simple methods for the fabrication of He II refilling devices, He II flow has been studied through filters made from various fine powders (oxides and metals, grain sizes in the range 0.05–2 μm) by compacting them under pressure. The results obtained for the different states of He II flow, especially in the “breakthrough” and “easy flow” range, are explained by the fountain effect, He II hydrodynamics and the choking effect. According to the results, pressedpowder filters can be classified into three groups with different flow characteristics, of which the “good transfer filters” with a behaviour neatly described by simple theory are suitable for use in He II refilling devices.