Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

A sustainable tourism development in Alacati, Turkey : (Re)invention of public space with clean energy

Although there is an increasing recognition of the impacts of climate change on communities, residents often resist changing their lifestyle to reduce the effects of the problem. By using a landscape architectural design medium, this paper argues that public space, when designed as an ecological system, has the capacity to create social and environmental change and to increase the quality of the human environment. At the same time, this ecological system can engage residents, enrich the local economy, and increase the social network. Through methods of design, research and case study analysis, an alternative master plan is proposed for a sustainable tourism development in Alacati, Turkey. Our master plan uses local geographical, economic and social information within a sustainable landscape architectural design scheme that addresses the key issues of ecology, employment, public space and community cohesion. A preliminary community empowerment model (CEM) is proposed to manage the designs. The designs address: the coexistence of local agricultural and sustainable energy generation; state of the art water management; and the functional and sustainable social and economic interrelationship of inhabitants, NGOs, and local government.

A sustainable tourism development in Alacati, Turkey: (Re) invention of public space with clean energy

Although there is an increasing recognition of the impacts of climate change on communities, residents often resist changing their lifestyle to reduce the effects of the problem. By using a landscape architectural design medium, this paper argues that public space, when designed as an ecological system, has the capacity to create social and environmental change and to increase the quality of the human environment. At the same time, this ecological system can engage residents, enrich the local economy, and increase the social network. Through methods of design, research and case study analysis, an alternative master plan is proposed for a sustainable tourism development in Alacati, Turkey. Our master plan uses local geographical, economic and social information within a sustainable landscape architectural design scheme that addresses the key issues of ecology, employment, public space and community cohesion. A preliminary community empowerment model (CEM) is proposed to manage the designs. The designs address: the coexistence of local agricultural and sustainable energy generation; state of the art water management; and the functional and sustainable social and economic interrelationship of inhabitants, NGOs, and local government.

A comprehensive analysis of parameter settings for novelty-biased cumulative gain

In the TREC Web Diversity track, novelty-biased cumulative gain (α-NDCG) is one of the official measures to assess retrieval performance of IR systems. The measure is characterised by a parameter, α, the effect of which has not been thoroughly investigated. We find that common settings of α, i.e. α=0.5, may prevent the measure from behaving as desired when evaluating result diversification. This is because it excessively penalises systems that cover many intents while it rewards those that redundantly cover only few intents. This issue is crucial since it highly influences systems at top ranks. We revisit our previously proposed threshold, suggesting α be set on a query-basis. The intuitiveness of the measure is then studied by examining actual rankings from TREC 09-10 Web track submissions. By varying α according to our query-based threshold, the discriminative power of α-NDCG is not harmed and in fact, our approach improves α-NDCG's robustness. Experimental results show that the threshold for α can turn the measure to be more intuitive than using its common settings.

Urban growth in the Kathmandu Valley: The transformation of public space

Traditional towns of the Kathmandu Valley boast a fine provision of public spaces in their neighbourhoods. Historically, a hierarchy of public space has been distributed over the entire town with each neighbourhood centered around more or less spacious public squares. However, rapid growth of these towns over the past decades has resulted in haphazard development of new urban areas with little provision of public space. Recent studies indicate that the loss of public space is a major consequence of the uncontrolled urban growth of the Kathmandu Valley and its new neighbourhoods. This paper reviews the current urban growth of the Kathmandu Valley and its impact on the development of public space in new neighbourhoods. The preliminary analysis of the case study of three new neighbourhoods shows that the formation and utilization of neighbourhood public space exhibit fundamental differences from those found in the traditional city cores. The following key issues are identified in this paper: a) Governance and regulations have been a challenge to regulate rapid urban growth; b) The current pattern of neighbourhood formation is found to be different from that of traditional neighbourhoods due to the changes with rapid urban development; c) Public spaces have been compromised in both planned and unplanned new neighbourhoods in terms of their quantity and quality; d) The changing provision of public space has contributed to its changing use and meaning; and e) The changing demographic composition, changing society and life style have had direct impact on the declining use of public space. Moreover, the management of public spaces remains a big challenge due to their changing nature and the changing governance. The current transformation public space does not appear to be conducive, and has led to adversely changing social environment of the new neighbourhoods.

Territoriality and the regulation of public space in Favela Morro da Formiga, Rio de Janeiro

Public space in many communities around the world has been identified as over-regulated and devoid of social vibrancy. This research contributed new knowledge regarding the way local residents territorialise and take ownership of streets and open areas in a favela, or informal settlement, in Rio De Janeiro, Brazil. Findings showed that public spaces were only partly activated by spatial pattern or structure. User agency also played a significant role, despite recent regulatory and policing interventions in the favela. This may have important implications for new communities where design could allow for more flexible usage and thereby enhance social vibrancy.

Transformation of public space in contemporary urban neighbourhoods of Kathmandu Valley, Nepal: An investigation of changing provision, use and meaning

This research examined the transformation of public space in contemporary urban neighbourhoods of the Kathmandu Valley in Nepal. The development of neighbourhood public space remains a considerable challenge in the present changing context, with significant consequences for public life and social interaction. The findings will aid policy makers, urban planners and designers in addressing the adverse effects of the current urban growth and change, and in winning back public space for the well-being of the local community.

TrainYarn: Probing perceptions of social space in urban commuter trains

We studied the ways that urban commuter train passengers experience their journeys. We present the design process and in-situ evaluation of TrainYarn, a mobile app prototype designed to facilitate social interaction between co-located urban train passengers. Through the deployment of the prototype, we sought to probe perceptions of social space with a view to positively impact the assessment of public transport. Our results support that our target users saw value in the use of TrainYarn, perceiving it as emancipatory, in alignment with their communicative needs, and having the ability to transform their perceptions of social space. To further inform future research and practice, we put forward a series of design recommendations.

Analysis of parameter uncertainty and sensitivity in PCPF-1 modeling for predicting concentrations of rice herbicides

This paper demonstrates the procedures for probabilistic assessment of a pesticide fate and transport model, PCPF-1, to elucidate the modeling uncertainty using the Monte Carlo technique. Sensitivity analyses are performed to investigate the influence of herbicide characteristics and related soil properties on model outputs using four popular rice herbicides: mefenacet, pretilachlor, bensulfuron-methyl and imazosulfuron. Uncertainty quantification showed that the simulated concentrations in paddy water varied more than those of paddy soil. This tendency decreased as the simulation proceeded to a later period but remained important for herbicides having either high solubility or a high 1st-order dissolution rate. The sensitivity analysis indicated that PCPF-1 parameters requiring careful determination are primarily those involve with herbicide adsorption (the organic carbon content, the bulk density and the volumetric saturated water content), secondary parameters related with herbicide mass distribution between paddy water and soil (1st-order desorption and dissolution rates) and lastly, those involving herbicide degradations. © Pesticide Science Society of Japan.

The effects of holding space on growth and survival of individually reared three-spot crab (Portunus sanguinolentus).

The problem of cannibalism in communally reared crabs can be eliminated by separating the growing crabs into holding compartments. There is currently no information on optimal compartment size for growing crabs individually. 136 second instar crablets (Portunus sanguinolentus) (C2 ca. 7-10 mm carapace width (CW)) were grown for 90 days in 10 different-sized opaque and transparent walled acrylic compartments. The base area for each compartment ranged from small (32 mm × 32 mm) to large (176 mm × 176 mm). Effects of holding space and wall transparency on survival, CW, moult increment, intermoult period and average weekly gain (AWG) were examined. Most crabs reached instars C9-C10 (50-70 mm CW) by the end of experiment. The final survival rate in the smallest compartment was 25% mainly due to moult-related mortality predominantly occurring at the C9 instar. However, crabs in these smaller compartments had earlier produced significantly larger moult increments from instar to instar than those in the larger compartments (P < 0.05). Crabs in the smaller compartments (<65 mm × 65 mm) also showed significantly longer moult periods (P < 0.05). The net result was that AWG in CW was 5.22 mm week-1 for the largest compartment and 5.15 mm week-1 in smallest and did not differ significantly between compartment size groups (P = 0.916). Wall transparency had no impact on survival (P = 0.530) but a slight impact on AWG (P = 0.014). Survival rate was the best indicator of minimum acceptable compartment size (?43 mm × 43 mm) for C10 crablets because below this size death occurred before growth rate was significantly affected. For further growth, it would be necessary to transfer the crablets to larger compartments.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

A novel approach to 6-DOF adaptive trajectory tracking control of an AUV in the presence of parameter uncertainties

In this paper, the trajectory tracking control of an autonomous underwater vehicle (AUVs) in six-degrees-of-freedom (6-DOFs) is addressed. It is assumed that the system parameters are unknown and the vehicle is underactuated. An adaptive controller is proposed, based on Lyapunov׳s direct method and the back-stepping technique, which interestingly guarantees robustness against parameter uncertainties. The desired trajectory can be any sufficiently smooth bounded curve parameterized by time even if consist of straight line. In contrast with the majority of research in this field, the likelihood of actuators׳ saturation is considered and another adaptive controller is designed to overcome this problem, in which control signals are bounded using saturation functions. The nonlinear adaptive control scheme yields asymptotic convergence of the vehicle to the reference trajectory, in the presence of parametric uncertainties. The stability of the presented control laws is proved in the sense of Lyapunov theory and Barbalat׳s lemma. Efficiency of presented controller using saturation functions is verified through comparing numerical simulations of both controllers.

Meaning of public space and sense of community: The case of new neighbourhoods in the Kathmandu Valley

This paper examines the meaning of public space and sense of community among neighbourhood residents in the changing urban context of the Kathmandu Valley in Nepal. Two new neighbourhoods were selected for the purpose of this study with data collected from interviews with the residents. The study has found that most residents of the new neighbourhoods have an understanding of the significance of public space in community life. However, such understandings are based less on the actual use of public space. The existing public spaces in these neighbourhoods are less successful in offering a meaning to the residents, due to their poor development and the lack of active use. Despite these changes, some residents believe they have developed a sense of community, which is an outcome of other individual factors than the use of public space. It is argued that the role of contemporary neighbourhood public space in fostering a sense of community appears to be less significant in the valley’s present context.