Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Effectiveness of on-line resources to enhance student learning and engagement

BACKGROUND For engineering graduates to be work-ready with marketable skills they must not only be well-versed with engineering science and its applications, but also able to adapt to using commercial software that is widely used in engineering practice. Hydrological/hydraulic modelling is one aspect of engineering practice which demands the ability to apply fundamentals into design and construction using software. The user manuals for such software are usually tailored for the experienced engineer but not for undergraduates who typically are novices to concepts of modelling and software tools. As the focus of a course such as Advanced Water Engineering is on the wider aspects of engineering application of hydrological and hydraulic concepts, it is ineffective for the lecturers to direct the students to user manuals as students have neither the time nor the desire to sift through numerous pages in a manual. An alternative and efficient way to demonstrate the use of the software is enabling students to develop a model to simulate real-world scenario using the tools of the software and directing them to make informed decisions based on outcomes. PURPOSE Past experience of the lecturer showed that the resources available for the students left a knowledge gap leading to numerous student queries outside contact hours. The purpose of this study is to assess how effective purpose-built video resources can be in supplementing the traditional learning resources to enhance student learning. APPROACH Short-length animated video clips comprising guided step-by-step instructions were prepared using screen capture software to capture screen activity and later edited to focus on specific features using pop-up annotations; Vocal narration was purposely excluded to avoid disturbances due to noise and allow different learning paces of individual students. The video clips were made available to the students alongside the traditional resources/approaches such as in-class demonstrations, guideline notes, and tips for efficient and error-free procedural descriptions. The number of queries the lecturer received from the student cohort outside the lecture times was recorded. An anonymous survey to assess the usefulness and adequacy of the courseware was conducted. OUTCOMES While a significant decline in the number of student queries was noted, an overwhelming majority of the survey respondents confirmed the usefulness of the purpose-developed courseware. CONCLUSIONS/RECOMMENDATIONS/SUMMARY The survey and lecturer’s experience indicated that animated demonstration video clips illustrating the various steps involved in developing hydrologic and hydraulic models and simulating design scenarios is an effective supplement for traditional learning resources. Among the many advantages of the custom-made video clips as a learning resource are that they (1) highlight the aspects that are important to undergraduate learning but not available in the software manuals as the latter are designed for more mature users/learners; (2) provide short, to-the point communication in a step-by-step manner; (3) allow students flexibility to self-learn at their own pace; (4) enhance student learning; and (5) enable time savings for the lecturer in the long term by avoiding queries of a repetitive nature. It is expected that these newly developed resources will be improved to incorporate students’ suggestions before being offered to future cohorts of students. The concept can also be expanded to other relevant courses where animated demonstrations of key modelling steps are beneficial to student learning.

A strong lightweight authentication protocol for low-cost RFID systems

RFID is an important technology that can be used to create the ubiquitous society. But an RFID system uses open radio frequency signal to transfer information and this leads to pose many serious threats to its privacy and security. In general, the computing and storage resources in an RFID tag are very limited and this makes it difficult to solve its secure and private problems, especially for low-cost RFID tags. In order to ensure the security and privacy of low-cost RFID systems we propose a lightweight authentication protocol based on Hash function. This protocol can ensure forward security and prevent information leakage, location tracing, eavesdropping, replay attack and spoofing. This protocol completes the strong authentication of the reader to the tag by twice authenticating and it only transfers part information of the encrypted tag’s identifier for each session so it is difficult for an adversary to intercept the whole identifier of a tag. This protocol is simple and it takes less computing and storage resources, it is very suitable to some low-cost RFID systems.

Multifractal analyses of daily rainfall time series in Pearl River basin of China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K(q)K(q) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter HH from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h(2)h(2) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K(2)K(2) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

Fractal and complex network analyses of protein molecular dynamics

Based on protein molecular dynamics, we investigate the fractal properties of energy, pressure and volume time series using the multifractal detrended fluctuation analysis (MF-DFA) and the topological and fractal properties of their converted horizontal visibility graphs (HVGs). The energy parameters of protein dynamics we considered are bonded potential, angle potential, dihedral potential, improper potential, kinetic energy, Van der Waals potential, electrostatic potential, total energy and potential energy. The shape of the h(q)h(q) curves from MF-DFA indicates that these time series are multifractal. The numerical values of the exponent h(2)h(2) of MF-DFA show that the series of total energy and potential energy are non-stationary and anti-persistent; the other time series are stationary and persistent apart from series of pressure (with H≈0.5H≈0.5 indicating the absence of long-range correlation). The degree distributions of their converted HVGs show that these networks are exponential. The results of fractal analysis show that fractality exists in these converted HVGs. For each energy, pressure or volume parameter, it is found that the values of h(2)h(2) of MF-DFA on the time series, exponent λλ of the exponential degree distribution and fractal dimension dBdB of their converted HVGs do not change much for different proteins (indicating some universality). We also found that after taking average over all proteins, there is a linear relationship between 〈h(2)〉〈h(2)〉 (from MF-DFA on time series) and 〈dB〉〈dB〉 of the converted HVGs for different energy, pressure and volume.

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Interdependence between Greece and other European stock markets: A comparison of wavelet and VMD copula, and the portfolio implications

The interdependence of Greece and other European stock markets and the subsequent portfolio implications are examined in wavelet and variational mode decomposition domain. In applying the decomposition techniques, we analyze the structural properties of data and distinguish between short and long term dynamics of stock market returns. First, the GARCH-type models are fitted to obtain the standardized residuals. Next, different copula functions are evaluated, and based on the conventional information criteria and time varying parameter, Joe-Clayton copula is chosen to model the tail dependence between the stock markets. The short-run lower tail dependence time paths show a sudden increase in comovement during the global financial crises. The results of the long-run dependence suggest that European stock markets have higher interdependence with Greece stock market. Individual country’s Value at Risk (VaR) separates the countries into two distinct groups. Finally, the two-asset portfolio VaR measures provide potential markets for Greece stock market investment diversification.