Ergodic capacity of the slotted amplify and forward relay channel with finite relays

Abstract—In this paper we investigate the capacity of a general class of the slotted amplify and forward (SAF) relaying protocol where multiple, though a finite number of relays may transmit in a given cooperative slot and the relay terminals being half-duplex have a finite slot memory capacity. We derive an expression for the capacity per channel use of this generalized SAF channel assuming all source to relay, relay to destination and source to destination channel gains are independent and modeled as complex Gaussian. We show through the analysis of eigenvalue distributions that the increase in limiting capacity per channel use is marginal with the increase of relay terminals.

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to Real-Time Kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least-squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance-covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio-test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.

Bismuth in interplanetary dust

Samples of a large (~60 µm) chondritic porous (CP) aggregate collected from the stratosphere have been analysed in detail by analytical electron microscopy (AEM). Previous studies of CP aggregates have shown that they are extraterrestrial in origin1–3 and may be related to cometary debris4. CP aggregates are dissimilar to C1 and C2 carbonaceous chondrite matrices and many have not been significantly altered by thermal or radiation processes since their assembly5. We report here a high concentration of Bi2O3 grains within the large CP aggregate designated W7029* A (~60 µm) and suggest they formed by rapid heating (~300 °C) of elemental Bi grains within the aggregate during atmospheric entry. We examine the possibilities for terrestrial Bi contamination of CP aggregate W7029* A but judge them unlikely. Enrichment of elemental Bi within components of extraterrestrial materials is consistent with a nebula condensation model6 and implies that Bi within CP aggregate W7029* A may have formed at a late stage of the condensation process.

Poorly characterized phases in C2M carbonaceous chondrites : proposed structures and significance

Poorly characterized phases (PCP's) may constitute up to 30 volume percent of some C2M carbonaceous chondrite matrices [1] and are an important key to an understanding of matrix evolution. PCPs are usually fine-grained (

Electron petrography of fine-grained matrix in the Karoonda C4 carbonaceous chondrite

The study of matrices of rare Type 4 carbonaceous chondrites can reveal important information on parent body rnetamorp~ic processes and provide a comparison with processes on parent bodies of ordinary chc-idrites. Reflectance spectra (Tholen, 1984) from the two largest asteroids in the asteroid belt, Ceres and Pallas, suggest that they may be metamorphosed carbonaceous chondrites. These two asteroids constitute - onethird of the mass in the asteroid belt implying that type 4-6 carbonaceous chondrites are poorly represented in the meteorite collection and may be of considerable importance. The matrix of the C4 chondrite Karoonda has been investigated using a JEOL 2000FX analytical electron microscope (AEM) with an attached Tracor-Northem TN5500 energy dispersive spectrometer (EDS). In previous studies (Scott and Taylor, 1985; Fitzgerald, 1979; Van Schmus, 1969), the petrography of the Karoonda matrix has been described as consisting largely of coarse-grained (50-200 urn in size) olivine and plagioclase (20-100 um in size), associated with micrometer sized magnetite and rare sulphides. AEM observations on matrix show that in addition to these large grains, there is a significant fraction (10 vol%) of interstitial fine grained phases « 5 urn). The mineralogy of these fine-grained phases differs in some respects from that of the coarser-grained matrix identified by optical and SEM techniques (Scott and Taylor, 1985; Fitzgerald, 1979; Van Schmus, 1969). I~ particular crystals of two compositionally distinct pyroxenes « 2 urn in size) have been identified which have not been previously observed in Karoonda by other analytical techniques. Thin film microanalyses (Mackinnon et al., 1986) of these two pyroxenes indicate compositions consistent with augite and low-Ca pyroxene (- Fs27). Fine-grained anhedral olivine « 2 urn size) is the most abundant phase with composition -Fa29' This composition is essentially indistinguishable from that determined for coarser-grained matrix olivines using an electron microprobe (Scott and Taylor, 1985; Fitzgerald, 1979; Van Schmus, 1969). All olivines are associated with subhedral magnetites « 1 urn size) which contain significant Cr (- 2%) and Al (- 1%) as was also noted for larger sized Karoonda magnetites by Delaney et al. (1985). It has recently been suggested (Burgess et al., 1987) on the basis of sulphur release profiles for S-isotope analyses of Karoonda that CaS04 (anhydrite) may be present. However, no sulphate phase has, as yet, been identified in the matrix of Karoonda. Low magnification contrast images suggest that Karoonda may have a significant porosity within the fine-grained matrix fraction. Most crystals are anhedral and do not show evidence for significant compaction. Individual grains often show single point contact with other grains which result in abundant intergranular voids. These voids frequently contain epoxy which was used as part of the specimen preparation procedure due to the friable nature of the bulk sample.

Interstellar titanium-oxides in interplanetary dust

Interstellar gas abundances (Clayton et al., 1986) suggest that titanium may be bound up in dust and indeed, excess titanium in carbonaceous chondrites is attributed to mixing of interstellar and Solar System materials (Morton, 1974). Fine-grained chondritic interplanetary dust particles (lOPs) of cometary origin are relatively pristine early Solar System materials (Mackinnon and Rietmeijer, 1987; Rietmeijer, 1987) and show chemical and mineralogical signatures related to a pre-solar or nebular origin. For example, large OtH ratios suggest a presolar or interstellar dust component in some chondritic lOPs(Mackinnon and Rietmeijer, 1987). Ti/Si ratios (normalized to bulk CI) in lOPs and carbonaceous chondrite matrices exceed solar abundances but are similar to dust from comet Halley (Jessberger et al., 1987). The Ti-distribution in chondritic lOPs shows major, small-scale « 0.1 urn) variations (Flynn et al., 1978) consistent with heterogeneously distributed Ti-bearingphases. Analytical electron microscope (AEM) studies, in fact, have identified platey grains of Ti-metal, Ti407 and Ti s09 in two different lOPs (Mackinnon and Rietmeijer, 1987). The occurrence of Ti407 was related in situ low-temperature aqueous alteration and therefore implied the presence of BaTi03 (Rietmeijer and Mackinnon, 1984). Yet, the presence ofTis09 in an lOp which shows no evidence of aqueous alteration (Rietmeijer.and McKay, 1986) requires a different interpretation. The distribution of Ti-oxides in chondritic lOPs were investigated with ultra-microtomed thin sections of fluffy chondri tic lOP U2011*B (lSC allocation U2011C2) using a lEOL 2000FX AEM operating at an accelerating voltage of 200kV and with an attached Tracor Northern TN5500 energy dispersive spectrometer.

The clay-size fraction of CI chondrites Alais and Orgueil : an AEM study

CI chondrites are used pervasively in the meteorite literature as a cosmochemical reference point for bulk compositions[1], isotope analyses[2] and, within certain models of meteorite evolution, as an important component of an alteration sequence within the carbonaceous chondrite subset[3]. More recently, the chemical variablity of CI chondrite matrices (which comprise >80% of the meteorite), has been cited in discussions about the "chondritic" nature of spectroscopic data from P/comet Halley missions[4] and of chemical data from related materials such as interplanetary dust particles[5]. Most CI chondrites have been studied as bulk samples(e.g. major and trace element abundances)and considerable effort has also been focussed on accessory phases such as magnetites, olivine, sulphates and carbonates [6-8]. A number of early studies showed that the primary constituents of CI matrices are layer silicates and the most definitive structural study on powdered samples identified two minerals: montmorillonite and serpentine[9]. In many cases, as with the study by Bass[9],the relative scarcity of most CI chondrites restricts such bulk analyses to the Orgueil meteorite. The electron microprobe/SEM has been used on petrographic sections to more precisely define the "bulk" composition of at least four CI matrices[3], and as recently summarised by McSween[3], these data define a compositional trend quite different to that obtained for CM chondrite matrices. These "defocussed-beam" microprobe analyses average major element compositions over matrix regions ~lOOµm in diameter and provide only an approximation to silicate mineral composition(s) because their grain sizes are much less than the diameter of the beam. In order to (a) more precisely define the major element compositions of individual mineral grains within CI matrices, and (b)complement previous TEM studies [11,12], we have undertaken an analytical electron microscopy (AEM) study of Alais and Orgueil matrices.

Assessing performance and capability in the work place : focusing on essential skills and knowledge in student work placements

The determination of performance standards and assessment practices in regard to student work placements is an essential and important task. Inappropriate, inadequate, or excessively complex assessment tasks can influence levels of student engagement and the quality of learning outcomes. Critical to determining appropriate standards and assessment tasks is an understanding and knowledge of key elements of the learning environment and the extent to which opportunities are provided for students to engage in critical reflection and judgement of their own performance in the contexts of the work environment. This paper focuses on the development of essential skills and knowledge (capabilities) that provide evidence of learning in work placements by describing an approach taken in the science and technology disciplines. Assessment matrices are presented to illustrate a method of assessment for use within the context of the learning environment centred on work placements in science and technology. This study contributes to the debate on the meaning of professional capability, performance standards and assessment practices in work placement programs by providing evidence of an approach that can be adapted by other programs to achieve similar benefits. The approach may also be valuable to other learning contexts where capability and performance are being judged in situations that are outside a controlled teaching and learning environment i.e. in other life-wide learning contexts.

Titanium-oxide magneli phases in four chondritic porous interplanetary dust particles

Detailed analytical electron microscope analyses of four fine-grained chondritic porous interplanetary dust particles (IDPs)reveal the presence of titanium oxide Magneli phases, TinO2n-1 (n=4,5,6), and rare Ti-metal. The titanium minerals are indigenous to these chondritic IDPs. The association of Magneli phases, Ti-metal, and carbonaceous material in chondritic IDPs, along with the grain size distributions support in situ solid carbon gasification in these extraterrestrial particles. The active catalyst in this process is titanium metal that we infer may be of interstellar origin. This favorable catalysis uniquely leads to the formation of Magneli phases. As chondritic IDPs may be solid debris of short-period comets, our data indicate that nuclei of short-period comets may show distinctive chemical reactions that lead to Ti-mineral assemblages that typically include Magneli phases. The proposed model provides a plausible mechnism to explain the higher solid carbon content of chondritic IDPs relative to bulk carbon abundances typical for carbonaceous chondrite matrices that represent another type of more evolved, that is, metamorphosed, undifferentiated solar system bodies.

New phyllosilicate types in a carbonaceous chondrite matrix

CARBONACEOUS chondrites provide valuable information as they are the least altered examples of early Solar System material1. The matrix constitutes a major proportion of carbonaceous chondrites. Despite many past attempts, unambiguous identification of the minerals in the matrix has not been totally successful2. This is mainly due to the extremely fine-grained nature of the matrix phases. Recently, progress in the characterisation of these phases has been made by electron diffraction studies3,4. We present here the direct observation, by high resolution imaging, of phases in carbonaceous chondrite matrices. We used ion-thinned sections from the Murchison C2(M) meteorite for transmission electron microscopy. The Murchison matrix contains both ordered and disordered inter-growths of serpentine-like and brucite-like layers. Such mixed-layer structures are new types of layer silicates. © 1979 Nature Publishing Group.

Growth of confined cancer spheroids : a combined experimental marker, critical modelling approach

A critical step in the dissemination of ovarian cancer is the formation of multicellular spheroids from cells shed from the primary tumour. The objectives of this study were to apply bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer spheroids in vitro and simultaneously to build on a mathematical model describing the growth of multicellular spheroids in these biomimetic matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and grown for up to 4 weeks. Immunohistochemistry, imaging and growth analyses were used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel. The mathematical model was formulated as a free boundary problem in which each spheroid was treated as an incompressible porous medium. The functional forms used to describe the rates of cell proliferation and apoptosis were motivated by the experimental work and predictions of the mathematical model compared with the experimental output. This work aimed to establish whether it is possible to simulate solid tumour growth on the basis of data on spheroid size, cell proliferation and cell death within these spheroids. The mathematical model predictions were in agreement with the experimental data set and simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture duration and administration of a chemotherapeutic drug. Our computational model provides new perspectives on experimental results and has informed the design of new 3D studies of chemoresistance of multicellular cancer spheroids.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

High resolution transmission electron microscopy of the Murchison Carbonaceous Chondrite and the Kenna Ureilite

Fine-grained matrices in carbonaceous chondrites and small, micron-sized inclusions in achondrites can be characterized effectively using high resolution transmission electron micro­scopy (HRTEM).

Preparation of porous nanofibers from electrospun polyacrylonitrile/calcium carbonate composite nanofibers using porogen leaching technique

Production of nanofibrous polyacrylonitrile/calcium carbonate (PAN/CaCO3) nanocomposite web was carried out through solution electrospinning process. Pore generating nanoparticles were leached from the PAN matrices in hydrochloric acid bath with the purpose of producing an ultimate nanoporous structure. The possible interaction between CaCO3 nanoparticles and PAN functional groups was investigated. Atomic absorption method was used to measure the amount of extracted CaCO3 nanoparticles. Morphological observation showed nanofibers of 270–720 nm in diameter containing nanopores of 50–130 nm. Monitoring the governing parameters statistically, it was found that the amount of extraction (ε) of CaCO3was increased when the web surface area (a) was broadened according to a simple scaling law (ε = 3.18 a0.4). The leaching process was maximized in the presence of 5% v/v of acid in the extraction bath and 5 wt % of CaCO3 in the polymer solution. Collateral effects of the extraction time and temperature showed exponential growth within a favorable extremum at 50°C for 72 h. Concentration of dimethylformamide as the solvent had no significant impact on the extraction level.