Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

A simultaneous equations model of crash frequency by collision type for rural intersections

Safety at roadway intersections is of significant interest to transportation professionals due to the large number of intersections in transportation networks, the complexity of traffic movements at these locations that leads to large numbers of conflicts, and the wide variety of geometric and operational features that define them. A variety of collision types including head-on, sideswipe, rear-end, and angle crashes occur at intersections. While intersection crash totals may not reveal a site deficiency, over exposure of a specific crash type may reveal otherwise undetected deficiencies. Thus, there is a need to be able to model the expected frequency of crashes by collision type at intersections to enable the detection of problems and the implementation of effective design strategies and countermeasures. Statistically, it is important to consider modeling collision type frequencies simultaneously to account for the possibility of common unobserved factors affecting crash frequencies across crash types. In this paper, a simultaneous equations model of crash frequencies by collision type is developed and presented using crash data for rural intersections in Georgia. The model estimation results support the notion of the presence of significant common unobserved factors across crash types, although the impact of these factors on parameter estimates is found to be rather modest.

A parallel computation of power system equations

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III and P4 classes of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving power systems network equations with SSE and discuss advantages and disadvantages of this approach.

SSE based parallel solution for power systems network equations

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III class of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving power systems network equations with SSE and discuss advantages and disadvantages of this approach.

Generation evolution in GA application on railway traffic control

This paper presents a Genetic Algorithms (GA) approach to resolve traffic conflicts at a railway junction. The formulation of the problem for the suitable application of GA will be discussed and three neighborhoods have been proposed for generation evolution. The performance of the GA is evaluated by computer simulation. This study paves the way for more applications of artificial intelligence techniques on a rather conservative industry.

Comparing charge transport predictions for a ternary electrolyte using the Maxwell–Stefan and Nernst–Planck equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.

Estimation of parameters for macroparasite population evolution using approximate Bayesian computation

We estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate Bayesian computation (ABC). The immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted. With very limited data, process rates are inferred reasonably precisely. Modeling involves a three variable Markov process for which the observed data likelihood is computationally intractable. ABC methods are particularly useful when the likelihood is analytically or computationally intractable. The ABC algorithm we present is based on sequential Monte Carlo, is adaptive in nature, and overcomes some drawbacks of previous approaches to ABC. The algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the Markov process model for experimental data. The fitted model explains the observed extra-binomial variation in terms of a zero-one immunity variable, which has a short-lived presence in the host.

An evolution of waterfront development in Malaysia

River has long been recognized as one of humanity’s most important natural resources. It is one of the most important of all the natural resources necessary to ensure human health and civilization. A close association between cities and water is inherent since the history of civilization and in fact, many urban cities in Malaysia are located close to river areas. The last two decades shown Malaysia has shifted development strategy from agricultural based to industrialization, and manufacturing industries have become the economy’s main source for the country until now. This transformation in 18th century is clearly shown that rapid urbanization, industrial and intensive agricultural activities, as well as wide-spread land development, have contributed to extensive changing of river functions for economy, national development and environment. In particular, river roles are become less significance for human life and river function limited only for transportation purposes only. So, viewed historically, waterfront development in Malaysia have undergone cycles of change over the decades and the latest in this pattern to more public purposes such as recreational and mixed used development. This paper aims to identify a transition of waterfront development in Malaysia from history time to modernization era and it would give a significance contribution for the research is currently on going.

Influence of historical landscapes, drainage evolution and ecological traits on patterns of genetic diversity in Southeast Asian freshwater snakehead fishes

Snakehead fishes in the family Channidae are obligate freshwater fishes represented by two extant genera, the African Parachannna and the Asian Channa. These species prefer still or slow flowing water bodies, where they are top predators that exercise high levels of parental care, have the ability to breathe air, can tolerate poor water quality, and interestingly, can aestivate or traverse terrestrial habitat in response to seasonal changes in freshwater habitat availability. These attributes suggest that snakehead fishes may possess high dispersal potential, irrespective of the terrestrial barriers that would otherwise constrain the distribution of most freshwater fishes. A number of biogeographical hypotheses have been developed to account for the modern distributions of snakehead fishes across two continents, including ancient vicariance during Gondwanan break-up, or recent colonisation tracking the formation of suitable climatic conditions. Taxonomic uncertainty also surrounds some members of the Channa genus, as geographical distributions for some taxa across southern and Southeast (SE) Asia are very large, and in one case is highly disjunct. The current study adopted a molecular genetics approach to gain an understanding of the evolution of this group of fishes, and in particular how the phylogeography of two Asian species may have been influenced by contemporary versus historical levels of dispersal and vicariance. First, a molecular phylogeny was constructed based on multiple DNA loci and calibrated with fossil evidence to provide a dated chronology of divergence events among extant species, and also within species with widespread geographical distributions. The data provide strong evidence that trans-continental distribution of the Channidae arose as a result of dispersal out of Asia and into Africa in the mid–Eocene. Among Asian Channa, deep divergence among lineages indicates that the Oligocene-Miocene boundary was a time of significant species radiation, potentially associated with historical changes in climate and drainage geomorphology. Mid-Miocene divergence among lineages suggests that a taxonomic revision is warranted for two taxa. Deep intra-specific divergence (~8Mya) was also detected between C. striata lineages that occur sympatrically in the Mekong River Basin. The study then examined the phylogeography and population structure of two major taxa, Channa striata (the chevron snakehead) and the C. micropeltes (the giant snakehead), across SE Asia. Species specific microsatellite loci were developed and used in addition to a mitochondrial DNA marker (Cyt b) to screen neutral genetic variation within and among wild populations. C. striata individuals were sampled across SE Asia (n=988), with the major focus being the Mekong Basin, which is the largest drainage basin in the region. The distributions of two divergent lineages were identified and admixture analysis showed that where they co-occur they are interbreeding, indicating that after long periods of evolution in isolation, divergence has not resulted in reproductive isolation. One lineage is predominantly confined to upland areas of northern Lao PDR to the north of the Khorat Plateau, while the other, which is more closely related to individuals from southern India, has a widespread distribution across mainland SE Asian and Sumatra. The phylogeographical pattern recovered is associated with past river networks, and high diversity and divergence among all populations sampled reveal that contemporary dispersal is very low for this taxon, even where populations occur in contiguous freshwater habitats. C. micropeltes (n=280) were also sampled from across the Mekong River Basin, focusing on the lower basin where it constitutes an important wild fishery resource. In comparison with C. striata, allelic diversity and genetic divergence among populations were extremely low, suggesting very recent colonisation of the greater Mekong region. Populations were significantly structured into at least three discrete populations in the lower Mekong. Results of this study have implications for establishing effective conservation plans for managing both species, that represent economically important wild fishery resources for the region. For C. micropeltes, it is likely that a single fisheries stock in the Tonle Sap Great Lake is being exploited by multiple fisheries operations, and future management initiatives for this species in this region will need to account for this. For C. striata, conservation of natural levels of genetic variation will require management initiatives designed to promote population persistence at very localised spatial scales, as the high level of population structuring uncovered for this species indicates that significant unique diversity is present at this fine spatial scale.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

An intelligent building model of sustainable architecture in a mechanism of open systems evolution

This paper argues a model of open systems evolution based on evolutionary thermodynamics and complex system science, as a design paradigm for sustainable architecture. The mechanism of open system evolution is specified in mathematical simulations and theoretical discourses. According to the mechanism, the authors propose an intelligent building model of sustainable design by a holistic information system of the end-users, the building and nature. This information system is used to control the consumption of energy and material resources in building system at microscopic scale, to adapt the environmental performance of the building system to the natural environment at macroscopic scale, for an evolutionary emergence of sustainable performance of buildings.

Processing load and the use of concrete representations and strategies for solving linear equations

This paper is a report of students' responses to instruction which was based on the use of concrete representations to solve linear equations. The sample consisted of 21 Grade 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as a reason.

The social media (r)evolution : Obama's political campaign

This paper addresses how social media was used to leverage votes in new media environments. Barack Obama’s social media campaign is analysed and illustrates how the Obama brand benefited from integrating social media into the campaign. Voting behaviour has changed; politicians are continually seeking new ways to communicate with their constituents. Voting on political ‘brands’ is based on an identity or image, rather than central issues. While political parties rely upon an integrated marketing communication (IMC) approach, with a focus on building the (political) brand of the party and brand relationships, communication is no longer fully controlled by the marketers.