Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Renewable energy sources and frequency regulation : survey and new perspectives

As the use of renewable energy sources (RESs) increases worldwide, there is a rising interest on their impacts on power system operation and control. An overview of the key issues and new challenges on frequency regulation concerning the integration of renewable energy units into the power systems is presented. Following a brief survey on the existing challenges and recent developments, the impact of power fluctuation produced by variable renewable sources (such as wind and solar units) on sysstem frequency performance is also presented. An updated LFC model is introduced, and power system frequency response in the presence of RESs and associated issues is analysed. The need for the revising of frequency performance standards is emphasised. Finally, non-linear time-domain simulations on the standard 39-bus and 24-bus test systems show that the simulated results agree with those predicted analytically.

The relationship between substrate metabolism, exercise and appetite control : does glycogen availability influence the motivation to eat, energy intake or food choice?

The way in which metabolic fuels are utilised can alter the expression of behaviour in the interests of regulating energy balance and fuel availability. This is consistent with the notion that the regulation of appetite is a psychobiological process, in which physiological mediators act as drivers of behaviour. The glycogenostatic theory suggests that glycogen availability is central in eliciting negative feedback signals to restore energy homeostasis. Due to its limited storage capacity, carbohydrate availability is tightly regulated and its restoration is a high metabolic priority following depletion. It has been proposed that such depletion may act as a biological cue to stimulate compensatory energy intake in an effort to restore availability. Due to the increased energy demand, aerobic exercise may act as a biological cue to trigger compensatory eating as a result of perturbations to muscle and liver glycogen stores. However, studies manipulating glycogen availability over short-term periods (1-3 days) using exercise, diet or both have often produced equivocal findings. There is limited but growing evidence to suggest that carbohydrate balance is involved in the short-term regulation of food intake, with a negative carbohydrate balance having been shown to predict greater ad libitum feeding. Furthermore, a negative carbohydrate balance has been shown to be predictive of weight gain. However, further research is needed to support these findings as the current research in this area is limited. In addition, the specific neural or hormonal signal through which carbohydrate availability could regulate energy intake is at present unknown. Identification of this signal or pathway is imperative if a casual relationship is to be established. Without this, the possibility remains that the associations found between carbohydrate balance and food intake are incidental.

Post-occupancy analysis of a Zero Energy Hojme (ZEH)

Zero energy buildings (ZEB) and zero energy homes (ZEH) are a current hot topic globally for policy makers (what are the benefits and costs), designers (how do we design them), the construction industry (can we build them), marketing (will consumers buy them) and researchers (do they work and what are the implications). This paper presents initial findings from actual measured data from a 9 star (as built), off-ground detached family home constructed in south-east Queensland in 2008. The integrated systems approach to the design of the house is analysed in each of its three main goals: maximising the thermal performance of the building envelope, minimising energy demand whilst maintaining energy service levels, and implementing a multi-pronged low carbon approach to energy supply. The performance outcomes of each of these stages are evaluated against definitions of Net Zero Carbon / Net Zero Emissions (Site and Source) and Net Zero Energy (onsite generation v primary energy imports). The paper will conclude with a summary of the multiple benefits of combining very high efficiency building envelopes with diverse energy management strategies: a robustness, resilience, affordability and autonomy not generally seen in housing.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Increasing underwater vehicle autonomy by reducing energy consumption

In this paper, we concern ourselves with finding a control strategy that minimizes energy consumption along a trajectory connecting two given configurations. We develop an algorithm, based on our previous work with the time optimal problem, which provides implementable control strategies that are energy efficient. We find an interesting correlation between the duration of these trajectories and the optimal duration. We present the algorithm, control strategy and experimental results from our test-bed vehicle.

Autonomous underwater vehicles: development and implementation of time and energy efficient trajectories

Autonomous underwater vehicles (AUVs) are increasingly used, both in military and civilian applications. These vehicles are limited mainly by the intelligence we give them and the life of their batteries. Research is active to extend vehicle autonomy in both aspects. Our intent is to give the vehicle the ability to adapt its behavior under different mission scenarios (emergency maneuvers versus long duration monitoring). This involves a search for optimal trajectories minimizing time, energy or a combination of both. Despite some success stories in AUV control, optimal control is still a very underdeveloped area. Adaptive control research has contributed to cost minimization problems, but vehicle design has been the driving force for advancement in optimal control research. We look to advance the development of optimal control theory by expanding the motions along which AUVs travel. Traditionally, AUVs have taken the role of performing the long data gathering mission in the open ocean with little to no interaction with their surroundings, MacIver et al. (2004). The AUV is used to find the shipwreck, and the remotely operated vehicle (ROV) handles the exploration up close. AUV mission profiles of this sort are best suited through the use of a torpedo shaped AUV, Bertram and Alvarez (2006), since straight lines and minimal (0 deg - 30 deg) angular displacements are all that are necessary to perform the transects and grid lines for these applications. However, the torpedo shape AUV lacks the ability to perform low-speed maneuvers in cluttered environments, such as autonomous exploration close to the seabed and around obstacles, MacIver et al. (2004). Thus, we consider an agile vehicle capable of movement in six degrees of freedom without any preference of direction.

Information dependencies between architects and services engineers for early design evaluation : a framework for an energy design tool for architects

Effective strategies for the design of effi cient and environmentally sensitive buildings require a close collaboration between architects and engineers in the design of the building shell and environmental control systems at the outset of projects. However, it is often not practical for engineers to be involved early on in the design process. It is therefore essential that architects be able to perform preliminary energy analyses to evaluate their proposed designs prior to the major building characteristics becoming fi xed. Subsequently, a need exists for a simplifi ed energy design tool for architects. This paper discusses the limitations of existing analysis software in supporting early design explorations and proposes a framework for the development of a tool that provides decision support by permitting architects to quickly assess the performance of design alternatives.

Engaging energy saving through motivation-specific social comparison

Comparison is widely used in research projects and commercial products whose goal is to motivate energy saving at home. This research builds on fundamental theories from social psychology in an attempt to shed light on how to motivate consumers to conserve energy by providing relevant people for social comparison depending on consumer’s motivation to compare. To support the research process, the mobile application EnergyWiz was developed through a theory-driven design approach. Along with other features EnergyWiz provides users with three types of social comparison – normative, one-on-one and ranking. The results of interviews with prospective users are used to derive design suggestions for relevant people for comparison (comparison subjects).

Sequential nonlinear manifold learning

The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorithms in real-time systems necessitates the development of sequential algorithms that perform feature extraction online. This paper presents an efficient online NLDR scheme, Sequential-Isomap, based on incremental singular value decomposition (SVD) and the Isomap method. Example simulations demonstrate the validity and significant potential of this technique in real-time applications such as autonomous systems.

An analytical method to solve a general class of nonlinear reactive transport models

Three recent papers published in Chemical Engineering Journal studied the solution of a model of diffusion and nonlinear reaction using three different methods. Two of these studies obtained series solutions using specialized mathematical methods, known as the Adomian decomposition method and the homotopy analysis method. Subsequently it was shown that the solution of the same particular model could be written in terms of a transcendental function called Gauss’ hypergeometric function. These three previous approaches focused on one particular reactive transport model. This particular model ignored advective transport and considered one specific reaction term only. Here we generalize these previous approaches and develop an exact analytical solution for a general class of steady state reactive transport models that incorporate (i) combined advective and diffusive transport, and (ii) any sufficiently differentiable reaction term R(C). The new solution is a convergent Maclaurin series. The Maclaurin series solution can be derived without any specialized mathematical methods nor does it necessarily involve the computation of any transcendental function. Applying the Maclaurin series solution to certain case studies shows that the previously published solutions are particular cases of the more general solution outlined here. We also demonstrate the accuracy of the Maclaurin series solution by comparing with numerical solutions for particular cases.

Plantar enthesopathy : thickening of the enthesis is correlated with energy dissipation of the plantar fat pad during walking

Background: The enthesis of the plantar fascia is thought to play an important role in stress dissipation. However, the potential link between entheseal thickening characteristic of enthesopathy and the stress-dissipating properties of the intervening plantar fat pad have not been investigated. Purpose: This study was conducted to identify whether plantar fat pad mechanics explain variance in the thickness of the fascial enthesis in individuals with and without plantar enthesopathy. Study Design: Case-control study; Level of evidence, 3. Methods: The study population consisted of 9 patients with unilateral plantar enthesopathy and 9 asymptomatic, individually matched controls. The thickness of the enthesis of the symptomatic, asymptomatic, and a matched control limb was acquired using high-resolution ultrasound. The compressive strain of the plantar fat pad during walking was estimated from dynamic lateral radiographs acquired with a multifunction fluoroscopy unit. Peak compressive stress was simultaneously acquired via a pressure platform. Principal viscoelastic parameters were estimated from subsequent stress-strain curves. Results: The symptomatic fascial enthesis (6.7 ± 2.0 mm) was significantly thicker than the asymptomatic enthesis (4.2 ± 0.4 mm), which in turn was thicker than the enthesis (3.3 ± 0.4 mm) of control limbs (P < .05). There was no significant difference in the mean thickness, peak stress, peak strain, or secant modulus of the plantar fat pad between limbs. However, the energy dissipated by the fat pad during loading and unloading was significantly lower in the symptomatic limb (0.55 ± 0.17) when compared with asymptomatic (0.69 ± 0.13) and control (0.70 ± 0.09) limbs (P < .05). The sonographic thickness of the enthesis was correlated with the energy dissipation ratio of the plantar fat pad (r = .72, P < .05), but only in the symptomatic limb. Conclusion: The energy-dissipating properties of the plantar fat pad are associated with the sonograpic appearance of the enthesis in symptomatic limbs, providing a previously unidentified link between the mechanical behavior of the plantar fat pad and enthesopathy.

Motivating domestic energy conservation through comparative, community-based feedback in mobile and social media

The progress of technology has led to the increased adoption of energy monitors among household energy consumers. While the monitors available on the market deliver real-time energy usage feedback to the consumer, the format of this data is usually unengaging and mundane. Moreover, it fails to address consumers with different motivations and needs to save and compare energy. This paper presents a study that seeks to provide initial indications for motivation-specific design of energy-related feedback. We focus on comparative feedback supported by a community of energy consumers. In particular, we examine eco-visualisations, temporal self-comparison, norm comparison, one-on-one comparison and ranking, whereby the last three allow us to explore the potential of socialising energy-related feedback. These feedback types were integrated in EnergyWiz – a mobile application that enables users to compare with their past performance, neighbours, contacts from social networking sites and other EnergyWiz users. The application was evaluated in personal, semi-structured interviews, which provided first insights on how to design motivation-related comparative feedback.

Solar energy : utilization in building operations

In the face of increasing concern over global warming and climate change, interest in the utilizzation of solar energy for building operations is rapidly growing. In this entry, the importance of using renewable energy in building operations is first introduced. This is followed by a general overview on the energy from the sun and the methods to utilize solar energy. Possible applications of solar energy in building operations are then discussed, which include the use of solar energy in the forms of daylighting, hot water heating, space heating and cooling, and building-integrated photovoltaics.