On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

An advanced fuzzy Bayesian-based FMEA approach for assessing maritime supply chain risks

This paper aims to develop a novel model to assess the risk factors of maritime supply chains by incorporating a fuzzy belief rule approach with Bayesian networks. The new model, compared to traditional risk analysis methods, has the capability of improving result accuracy under a high uncertainty in risk data. A real case of a world leading container shipping company is investigated, and the research results reveal that among the most significant risk factors are transportation of dangerous goods, fluctuation of fuel price, fierce competition, unattractive markets, and change of exchange rates in sequence. Such findings will provide useful insights for accident prevention

Dynamics of conduction blocks in a model of paced cardiac tissue

We study numerically the dynamics of conduction blocks using a detailed electrophysiological model. We find that this dynamics depends critically on the size of the paced region. Small pacing regions lead to stationary conduction blocks while larger pacing regions can lead to conduction blocks that travel periodically towards the pacing region. We show that this size-dependence dynamics can lead to a novel arrhythmogenic mechanism. Furthermore, we show that the essential phenomena can be captured in a much simpler coupled-map model.Comment: 8 pages 6 figure

Use of evidential reasoning for eliciting bayesian subjective probabilities in human reliability analysis: A maritime case

Modelling the interdependencies among the factors influencing human error (e.g. the common performance conditions (CPCs) in Cognitive Reliability Error Analysis Method (CREAM)) stimulates the use of Bayesian Networks (BNs) in Human Reliability Analysis (HRA). However, subjective probability elicitation for a BN is often a daunting and complex task. To create conditional probability values for each given variable in a BN requires a high degree of knowledge and engineering effort, often from a group of domain experts. This paper presents a novel hybrid approach for incorporating the evidential reasoning (ER) approach with BNs to facilitate HRA under incomplete data. The kernel of this approach is to develop the best and the worst possible conditional subjective probabilities of the nodes representing the factors influencing HRA when using BNs in human error probability (HEP). The proposed hybrid approach is demonstrated by using CREAM to estimate HEP in the maritime area. The findings from the hybrid ER-BN model can effectively facilitate HEP analysis in specific and decision-making under uncertainty in general

A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Mass movement susceptibility mapping using satellite optical imagery compared with InSAR monitoring: Zigui County, Three Gorges region, China

Mass movements on steep slopes are a major hazard to communities and infrastructure in the Three Gorges region, China. Developing susceptibility maps of mass movements is therefore very important in both current and future land use planning. This study employed satellite optical imagery and an ASTER GDEM (15 m) to derive various parameters (namely geology; slope gradient; proximity to drainage networks and proximity to lineaments) in order to create a GIS-based map of mass movement susceptibility. This map was then evaluated using highly accurate deformation signals processed using the Persistent Scatterer (PS) InSAR technique. Areas of high susceptibility correspond well to points of high subsidence, which provides a strong support of our susceptibility map

Anomalous thermoelectric effects of ZrTe5_{5} in and beyond the quantum limit

Thermoelectric effects are more sensitive and promising probes to topological properties of emergent materials, but much less addressed compared to other physical properties. Zirconium pentatelluride (ZrTe$_{5}$) has inspired active investigations recently because of its multiple topological nature. We study the thermoelectric effects of ZrTe$_{5}$ in a magnetic field and find several anomalous behaviors. The Nernst response has a steplike profile near zero field when the charge carriers are electrons only, suggesting the anomalous Nernst effect arising from a nontrivial profile of Berry curvature. Both the thermopower and Nernst signal exhibit exotic peaks in the strong-field quantum limit. At higher magnetic fields, the Nernst signal has a sign reversal at a critical field where the thermopower approaches to zero. We propose that these anomalous behaviors can be attributed to the Landau index inversion, which is resulted from the competition of the $\sqrt{B}$ dependence of the Dirac-type Landau bands and linear-$B$ dependence of the Zeeman energy ($B$ is the magnetic field). Our understanding to the anomalous thermoelectric properties in ZrTe$_{5}$ opens a new avenue for exploring Dirac physics in topological materials.Comment: 6 pages, 4 figure