A superdirective 3-element array for adaptive beamforming

A small array composed of three monopole elements with very small element spacing on the order of λ/6 to λ/20 is considered for application in adaptive beamforming. The properties of this 3-port array are governed by strong mutual coupling. It is shown that for signal-to-noise maximization, it is not sufficient to adjust the weights to compensate for the effects of mutual coupling. The necessity for a RF-decoupling network (RF-DN) and its simple realization are shown. The array with closely spaced elements together with the RF-DN represents a superdirective antenna with a directivity of more than 10 dBi. It is shown that the required fractional frequency bandwidth and the available unloaded Q of the antenna and RF-DN structure determine the lower limit for the element spacing.

Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.

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.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Valorization of solid tire wastes available in Bangladesh by thermal treatment

In this study available solid tire wastes in Bangladesh were characterized through proximate and ultimate analyses, gross calorific values and thermogravimetric analysis to investigate their suitability as feedstock for thermal recycling by pyrolysis technology. A new approach in heating system, fixedbed fire-tube heating pyrolysis reactor has been designed and fabricated for the recovery of liquid hydrocarbons from solid tire wastes. The tire wastes were pyrolysed in the internally heated fixed-bed fire-tube heating reactor and maximum liquid yield of 46-55 wt% of solid tire waste was obtained at a temperature of 475 oC, feed size 4 cm3, with a residence time of 5 s under N2 atmosphere. The liquid products were characterized by physical properties, elemental analysis, FT-IR, 1H-NMR, GC MS techniques and distillation. The results show that the liquid products are comparable to petroleum fuels whereas fractional distillations and desulphurization are essential to be used as alternative for diesel engine fuels.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

The effect of Tenofovir on vitamin D metabolism in HIV-infected adults is dependent on sex and ethnicity

Background: Tenofovir has been associated with renal phosphate wasting, reduced bone mineral density, and higher parathyroid hormone levels. The aim of this study was to carry out a detailed comparison of the effects of tenofovir versus non-tenofovir use on calcium, phosphate and, vitamin D, parathyroid hormone (PTH), and bone mineral density. Methods: A cohort study of 56 HIV-1 infected adults at a single centre in the UK on stable antiretroviral regimes comparing biochemical and bone mineral density parameters between patients receiving either tenofovir or another nucleoside reverse transcriptase inhibitor. Principal Findings: In the unadjusted analysis, there was no significant difference between the two groups in PTH levels (tenofovir mean 5.9 pmol/L, 95% confidence intervals 5.0 to 6.8, versus non-tenofovir; 5.9, 4.9 to 6.9; p = 0.98). Patients on tenofovir had significantly reduced urinary calcium excretion (median 3.01 mmol/24 hours) compared to non-tenofovir users (4.56; p,0.0001). Stratification of the analysis by age and ethnicity revealed that non-white men but not women, on tenofovir had higher PTH levels than non-white men not on tenofovir (mean difference 3.1 pmol/L, 95% CI 5.3 to 0.9; p = 0.007). Those patients with optimal 25-hydroxyvitamin D (.75 nmol/L) on tenofovir had higher 1,25-dihydroxyvitamin D [1,25(OH)2D] (median 48 pg/mL versus 31; p = 0.012), fractional excretion of phosphate (median 26.1%, versus 14.6;p = 0.025) and lower serum phosphate (median 0.79 mmol/L versus 1.02; p = 0.040) than those not taking tenofovir. Conclusions: The effects of tenofovir on PTH levels were modified by sex and ethnicity in this cohort. Vitamin D status also modified the effects of tenofovir on serum concentrations of 1,25(OH)2D and phosphate.

School based youth health nurses and a true health promotion approach : the Ottawa what?

Aim: The purpose of this research is to examine School Based Youth Health Nurses experience of a true health promotion approach. Background: The School Based Youth Health Nurse Program is a state-wide school nursing initiative in Queensland, Australia. The program employs more than 120 fulltime and fractional school nurses who provide health services in state high schools. The role incorporates two primary components: individual health consultations and health promotion strategies. Design/Methods: This study is a retrospective inquiry generated from a larger qualitative research project about the experience of school based youth health nursing. The original methodology was phenomenography. In-depth interviews were conducted with sixteen school nurses recruited through purposeful and snowball sampling. This study accesses a specific set of raw data about School Based Youth Health Nurses experience of a true health promotion approach. The Ottawa Charter for Health Promotion (1986) is used as a framework for deductive analysis. Results: The findings indicate school nurses have neither an adverse or affirmative conceptual experience of a true health promotion approach and an adverse operational experience of a true health promotion approach based on the action areas of the Ottawa Charter. Conclusions: The findings of this research are important because they challenge the notion that school nurses are the most appropriate health professionals to undertake a true health promotion approach. If school nurses are the most appropriate health professionals to do a true health promotion approach, there are implications for recruitment and training and qualifications. If school nurses are not, who are the most appropriate health professionals to do school health promotion? Implications for Practice: These findings can be applied to other models of school nursing in Australia which emphasises a true health promotion approach because they relate specifically to school nurses’ experience of a true health promotion approach.

Re-melting of Bi-2212/Ag laminated tapes by partial melting process

Bi-2212 tapes are prepared by a combination of dip-coating and partial melt processing. We investigate the effect of re-melting of those tapes by partial melting followed by slow cooling on the structure and superconducting properties. Microstructural studies of re-melted samples show that they have the same overall composition as partially melted tapes. However, the fractional volumes of the secondary phases differ and the amounts and distribution of the secondary phases have a significant effect on the critical current. Critical current of Bi-2212/Ag tapes strongly depends on the maximum processing temperature. Initial J(c)'s of the tapes, which are partially melted, then slowly solidified at optimum conditions and finally post-annealed in an inert atmosphere, are up to 10.4 x 10(3) A/cm(2). It is found that the maximum processing temperature at initial partial melting has an influence on the optimum re-heat treatment conditions for the tapes. Re-melted tapes processed at optimum conditions recover superconducting properties after post-annealing in an inert atmosphere: the J(c) values of the tapes are about 80-110% of initial J(c)'s of those tapes.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Zircon chronochemistry of high heat-producing granites in Queensland and Europe

High heat-producing granites (HHPGs) are reservoir rocks for enhanced geothermal systems (EGS), yet the origins of their anomalous chemistry remain poorly understood. To gain a better understanding of the characteristic distribution of elemental depletions and enrichments (focussing on U, Th & K) within granite suites of different heritage and tectonic setting, and the processes that lead to these enrichments, we are undertaking a systematic accessory-mineral chronochemical study of two suites of S- and I-type granites in northern Queensland, as well as two archetypal HHPGs in Cornwall, England (S-type) and Soultz-sous- Forêts, France (I-type). Novel zircon LA-ICP-MS chronochemical methods will later be underpinned by a systematic petrographic, scanning electron microscope (SEM), and electron microprobe (EPMA) study of all the REE-Y-Th-U-rich accessory minerals to fully characterise how the composition, textural distributions and associations change with rock chemistry between and among the suites. Preliminary results indicate that zircons with inherited ages do not have anomalously high U (>1000 ppm) & Th (>400 ppm) values (Ahrens, 1965). Instead, enrichment in these HPE is seen in zircons dated to around the time of magmatic emplacement. These results indicate that enrichment arose primarily through fractional crystallisation of the granitic magmas. Our results support the suggestion that a source pre-enriched in the HPEs does not appear to be fundamental for the formation of all HHPGs. Instead fractional crystallisation processes, and the accessory minerals formed in magmas of differing initial compositions, are the key controls on the levels of enrichment observed (e.g. Champion & Chappell, 1992; Chappell & Hine, 2006). One implication is that the most fractionated granites may not be the most enriched in the HPEs and therefore prospective to future EGS development.