Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Does metabolic compensation explain the majority of less-than-expected weight loss in obese adults during a short-term severe diet and exercise intervention?

Objective: We investigated to what extent changes in metabolic rate and composition of weight loss explained the less-than-expected weight loss in obese men and women during a diet-plus-exercise intervention. Design: 16 obese men and women (41 ± 9 years; BMI 39 ± 6 kg/m2) were investigated in energy balance before, after and twice during a 12-week VLED (565–650 kcal/day) plus exercise (aerobic plus resistance training) intervention. The relative energy deficit (EDef) from baseline requirements was severe (74-87%). Body composition was measured by deuterium dilution and DXA and resting metabolic rate (RMR) by indirect calorimetry. Fat mass (FM) and fat-free mass (FFM) were converted into energy equivalents using constants: 9.45 kcal/gFM and 1.13 kcal/gFFM. Predicted weight loss was calculated from the energy deficit using the '7700 kcal/kg rule'. Results: Changes in weight (-18.6 ± 5.0 kg), FM (-15.5 ± 4.3 kg), and FFM (-3.1 ± 1.9 kg) did not differ between genders. Measured weight loss was on average 67% of the predicted value, but ranged from 39 to 94%. Relative EDef was correlated with the decrease in RMR (R=0.70, P<0.01) and the decrease in RMR correlated with the difference between actual and expected weight loss (R=0.51, P<0.01). Changes in metabolic rate explained on average 67% of the less-than-expected weight loss, and variability in the proportion of weight lost as FM accounted for a further 5%. On average, after adjustment for changes in metabolic rate and body composition of weight lost, actual weight loss reached 90% of predicted values. Conclusion: Although weight loss was 33% lower than predicted at baseline from standard energy equivalents, the majority of this differential was explained by physiological variables. While lower-than-expected weight loss is often attributed to incomplete adherence to prescribed interventions, the influence of baseline calculation errors and metabolic down-regulation should not be discounted.

Is the unigram relevance model term independent? Classifying term dependencies in query expansion

This paper develops a framework for classifying term dependencies in query expansion with respect to the role terms play in structural linguistic associations. The framework is used to classify and compare the query expansion terms produced by the unigram and positional relevance models. As the unigram relevance model does not explicitly model term dependencies in its estimation process it is often thought to ignore dependencies that exist between words in natural language. The framework presented in this paper is underpinned by two types of linguistic association, namely syntagmatic and paradigmatic associations. It was found that syntagmatic associations were a more prevalent form of linguistic association used in query expansion. Paradoxically, it was the unigram model that exhibited this association more than the positional relevance model. This surprising finding has two potential implications for information retrieval models: (1) if linguistic associations underpin query expansion, then a probabilistic term dependence assumption based on position is inadequate for capturing them; (2) the unigram relevance model captures more term dependency information than its underlying theoretical model suggests, so its normative position as a baseline that ignores term dependencies should perhaps be reviewed.

Long term transmission planning to meet renewable energy targets in Australia

Australia is rich in renewable energy resources such as wind, solar and geothermal. Geographical diversity of these renewable resources combined with developing climate change policies poses a great challenge for the long term interconnection planning. Intermittency of wind and solar potentially driving the development of new transmission lines bring additional complexity to power system operations and planning. This paper provides an overview of generation and transmission planning studies in Australia to meet 20% renewable energy target by 2020. Appraisal of the effectiveness of dispersed energy storage, non schedulable peaking plants, wide area controls and demand management techniques to aid the penetration of renewables is presented in this paper

Residential property investment : assessing home ownership long term viability

Home purchase and ownership is seen by the majority of Australians as the basis for a sound investment strategy and to seciure their long term retirement goals. Although home ownership rates in Australia are in excess of 65% of the population, there have been doubts raised as to the effectiveness of purchasing a house as the main source of retirement income. The main issue with this approach is that the house has to be sold to gain access to these funds or the owners have to take out a reverse mortgage to access the capital tied up in their home, which can be more expensive than selling. This paper will carryout a detailed analysis of a number of investment options to determine the effectiveness of home purchase as a long term investment vehicle. This study has found that the long term investment in equities or managed superannuation funds can provide a greater retirement income than the purchase of a residential property for owner occupation

Corneal changes following short-term rigid contact lens wear

Purpose: The aim of this cross-over study was to investigate the changes in corneal thickness, anterior and posterior corneal topography, corneal refractive power and ocular wavefront aberrations, following the short term use of rigid contact lenses. Method: Fourteen participants wore 4 different types of contact lenses (RGP lenses of 9.5 mm and 10.5 mm diameter, and for comparison a PMMA lens of 9.5 mm diameter and a soft silicone hydrogel lens) on 4 different days for a period of 8 h on each day. Measures were collected before and after contact lens wear and additionally on a baseline day. Results: Anterior corneal curvature generally showed a flattening with both of the RGP lenses and a steepening with the PMMA lens. A significant negative correlation was found between the change in corneal swelling and central and peripheral posterior corneal curvature (all p ≤ 0.001). RGP contact lenses caused a significant decrease in corneal refractive power (hyperopic shift) of approximately 0.5 D. The PMMA contact lenses caused the greatest corneal swelling in both the central (27.92 ± 15.49 μm, p < 0.001) and peripheral (17.78 ± 12.11 μm, p = 0.001) corneal regions, a significant flattening of the posterior cornea and an increase in ocular aberrations (all p ≤ 0.05). Conclusion: The corneal swelling associated with RGP lenses was relatively minor, but there was slight central corneal flattening and a clinically significant hyperopic change in corneal refractive power after the first day of lens wear. The PMMA contact lenses resulted in significant corneal swelling and reduced optical performance of the cornea.