Comment on "correlated noise in a logistic growth model"

We argue the results published by Bao-Quan Ai et al [Phys. Rev E 67, 022903 (2003)] on "correlated noise in a logistic growth model " are not correct. Their conclusion that for larger values of the correlation parameter, lambda, the cell population is peaked at x=0, which denotes the high extinction rate is also incorrect. We find the reverse behaviour corresponding to their results, that increasing lambda, promotes the stable growth of tumour cells. In particular, their results for steady-state probability, as a function of cell number, at different correlation strengths, presented in figures 1 and 2 show different behaviour than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation at small values of cell number that the steady state probability increases as they increase the correlation parameter is also questionable. Another striking feature in their figures (1 and 3) is that for the same values of the parameter lambda and alpha, their simulation produces two different curves both qualitatively and quantitatively.

Single crystal CVD diamond growth strategy by the use of a 3D geometrical model: Growth on (113) oriented substrates

The quality of single crystal diamond obtained by microwave CVD processes has been drastically improved in the last 5 years thanks to surface pretreatment of the substrates [A. Tallaire, J. Achard, F. Silva, R.S. Sussmann, A. Gicquel, E. Rzepka, Physica Status Solidi (A) 201, 2419-2424 (2004); G. Bogdan, M. Nesladek, J. D'Haen, J. Maes, V.V. Moshchalkov, K. Haenen, M. D'Olieslaeger, Physica Status Solidi (A) 202, 2066-2072 (2005); M. Yamamoto, T. Teraji, T. Ito, Journal of Crystal Growth 285, 130-136 (2005)]. Additionally, recent results have unambiguously shown the occurrence of (110) faces on crystal edges and (113) faces on crystal corners [F. Silva, J. Achard, X. Bonnin, A. Michau, A. Tallaire, O. Brinza, A. Gicquel, Physica Status Solidi (A) 203, 3049-3055 (2006)]. We have developed a 3D geometrical growth model to account for the final crystal morphology. The basic parameters of this growth model are the relative displacement speeds of (111), (110) and (113) faces normalized to that of the (100) faces, respectively alpha, beta, and gamma. This model predicts both the final equilibrium shape of the crystal (i.e. after infinite growth time) and the crystal morphology as a function of alpha, beta, gamma, and deposition time.

An optimized operating point, deduced from the model, has been validated experimentally by measuring the growth rate in (100), (111), (110), and (113) orientations. Furthermore, the evolution of alpha, beta, gamma as a function of methane concentration in the gas discharge has been established. From these results, crystal growth strategies can be proposed in order, for example, to enlarge the deposition area. In particular, we will show, using the growth model, that the only possibility to significantly increase the deposition area is, for our growth conditions, to use a (113) oriented substrate. A comparison between the grown crystal and the model results will be discussed and characterizations of the grown film (Photoluminescence spectroscopy, EPR, SEM) will be presented. (C) 2008 Elsevier B.V. All rights reserved.

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant EFG method

A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported.

The Growth of US Credit Unions

The growth of US credit unions during the 1990s is investigated empirically, using univariate and multivariate cross sectional and panel estimation techniques. Univariate tests of the law of proportionate effect suggest that in general large credit unions grew faster than their smaller counterparts. On average credit unions with above-average growth in one period tended to experience below-average growth in the next. Smaller credit unions tended to have more variable growth than large ones. While credit unions share a common co-operative philosophy, they differ in terms of age profile, scope for membership growth, charter type and financial structure and performance. In estimations of a multivariate growth model, most of these characteristics are found to have a significant influence on the size-growth relationship. While large state chartered credit unions grew faster than their smaller counterparts, the reverse was true for federally chartered credit unions. In general, if larger credit unions grew faster than smaller ones, they tended to do so for specific reasons: because their charters were less restrictive, because they were more efficient, or because they had a financial structure that was more conducive to growth. Therefore credit union growth was not `random', but highly systematic.

Uncertainty, learning and growth

The paper extends Blackburn and Galindev's (Economics Letters, Vol. 79 (2003), pp. 417-421) stochastic growth model in which productivity growth entails both external and internal learning behaviour with a constant relative risk aversion utility function and productivity shocks. Consequently, the relationship between long-term growth and short-term volatility depends not only on the relative importance of each learning mechanism but also on a parameter measuring individuals' attitude towards risk.

Numerical analysis of stiffener runout sections

The recent trend of incorporating more composite material in primary aircraft structures has highlighted the vulnerability of stiffened aerostructures to through-thickness stresses, which may lead to delamination and debonding at the skin-stiffener interface, leading to collapse. Stiffener runout regions are particularly susceptible to this problem and cannot be avoided due to the necessity to terminate stiffeners at rib intersections or at cutouts, interrupting the stiffener load path. In this paper, experimental tests relating to two different stiffener runout specimens are presented and the failure modes of both specimens are discussed in detail. A thinner-skinned specimen showed sudden and unstable crack propagation, while a thicker-skinned specimen showed initially unstable but subsequent stable crack growth. Detailed finite element models of the two specimens are developed, and it is shown how such models can explain and predict the behaviour and failure mode of stiffener runouts. The models contain continuum shell elements to model the skin and stiffener, while cohesive elements using a traction-separation law are placed at the skin-stiffener interface to effectively model the debonding which promotes structural failure.

Prediction of failure and fracture mechanisms of polymeric composites using finite element analysis. Part 1:Particulate filled composites

Micro-mechanical analysis of polymeric composites provides a powerful means for the quantitative assessment of their bulk behavior. In this paper we describe a robust finite element model (FEM) for the micro-structural modeling of the behavior of particulate filled polymer composites under external loads. The developed model is applied to simulate stress distribution in polymer composites containing particulate fillers. Quantitative information about the magnitude and location of maximum stress concentrations obtained from these simulations is used to predict the dominant failure and crack growth mechanisms in these composites. The model predictions are compared with the available experimental data and also with the values found using other methods reported in the literature. These comparisons show the range of the validity of the developed model and its predictive potential.

Prediction of failure and fracture mechanisms of polymeric composites using finite element analysis. Part 2:Fiber reinforced composites

A robust finite element scheme for the micro-mechanical modeling of the behavior of fiber reinforced polymeric composites under external loads is developed. The developed model is used to simulate stress distribution throughout the composite domain and to identify the locations where maximum stress concentrations occur. This information is used as a guide to predict dominant failure and crack growth mechanisms in fiber reinforced composites. The differences between continuous fibers, which are susceptible to unidirectional transverse fracture, and short fibers have been demonstrated. To assess the validity and range of applicability of the developed scheme, numerical results obtained by the model are compared with the available experimental data and also with the values found using other methods reported in the literature. These comparisons show that the present finite element scheme can generate meaningful results in the analysis of fiber reinforced composites.

Incorporation of multiwalled carbon nanotubes to acrylic based bone cements: Effects on mechanical and thermal properties

Polymethyl methacrylate (PMMA) bone cement–multiwalled carbon nanotube (MWCNT) nanocomposites with a weight loading of 0.1% were prepared using 3 different methods of MWCNT incorporation. The mechanical and thermal properties of the resultant nanocomposite cements were characterised in accordance with the international standard for acrylic resin cements. The mechanical properties of the resultant nanocomposite cements were influenced by the type of MWCNT and method of incorporation used. The exothermic polymerisation reaction for the PMMA bone cement was significantly reduced when thermally conductive functionalised MWCNTs were added. This reduction in exotherm translated in a decrease in thermal necrosis index value of the respective nanocomposite cements, which potentially could reduce the hyperthermia experienced in vivo. The morphology and degree of dispersion of the MWCNTs in the PMMA matrix at different scales were analysed using scanning electron microscopy. Improvements in mechanical properties were attributed to the MWCNTs arresting/retarding crack propagation through the cement by providing a bridging effect into the wake of the crack, normal to the direction of crack growth. MWCNT agglomerations were evident within the cement microstructure, the degree of these agglomerations was dependent on the method used to incorporate the MWCNTs into the cement.

Hicks meets Hotelling: the direction of technical change in capital-resource economies

We analyze a two-sector growth model with directed technical change where man-made capital and exhaustible resources are essential for production. The relative profitability of factor-specific innovations endogenously determines whether technical progress will be capital- or resource-augmenting. We show that any balanced growth equilibrium features purely resource-augmenting technical change. This result is compatible with alternative specifications of preferences and innovation technologies, as it hinges on the interplay between productive efficiency in the final sector, and the Hotelling rule characterizing the efficient depletion path for the exhaustible resource. Our result provides sound micro-foundations for the broad class of models of exogenous/endogenous growth where resource-augmenting progress is required to sustain consumption in the long run, contradicting the view that these models are conceptually biased in favor of sustainability.

Fatigue performance of aircraft panels with novel skin buckling containment features

To increase structural efficiency of stiffened panels in an aircraft, it is plausible to introduce skin buckling containment features to increase the local skin stability and thus static strength performance. Introducing buckling containment features may also significantly influence the fatigue crack growth performance of the stiffened panel. This study focuses on the experimental demonstration of panel durability with skin bay buckling containment features. Through a series of fatigue crack growth tests on integrally machined aluminium alloy stiffened panels, the potential to simultaneously improve static strength performance and crack propagation behaviour is demonstrated. The introduction of prismatic buckling containment features which have yielded significant static strength performance gains have herein demonstrated potential fatigue life gains of up to + 63 per cent.

Atomic ordering in nano-layered FePt

Monte Carlo simulation of chemical ordering kinetics in nano-layered L1₀ AB binary intermetallics was performed. The study addressed FePt thin layers considered as a material for ultra-high-density magnetic storage media and revealed metastability of the L1₀ c-variant superstructure with monoatomic planes parallel to the surface and off-plane easy magnetization. The layers, originally perfectly ordered in a c-variant of the L1₀ superstructure, showed homogeneous disordering running in parallel with a spontaneous re-orientation of the monoatomic planes leading to a mosaic microstructure composed of a- and b-L1₀-variant domains. The domains nucleated heterogeneously on the surface of the layer and grew discontinuously inwards its volume. Finally, the domains relaxed towards an equilibrium microstructure of the system. Two “atomistic-scale” processes: (i) homogeneous disordering and (ii) nucleation of the a- and b-L1₀-variant domains showed characteristic time scales. The same was observed for the domain microstructure relaxation. The discontinuous domain growth showed no definite driving force and proceeded due to thermal fluctuations. The above complex structural evolution has recently been observed experimentally in epitaxially deposited thin films of FePt.

Aerospace Stiffened Panel Initial Sizing With Novel Skin Sub-Stiffening Features

The introduction of skin sub-stiffening features has the potential to modify the local stability and fatigue crack growth performance of stiffened panels. Proposed herein is a method to enable initial static strength sizing of panels with such skin sub-stiffening features. The method uses bespoke skin buckling coefficients, automatically generated by Finite Element analysis and thus limits the modification to the conventional aerospace panel initial sizing process. The approach is demonstrated herein and validated for prismatic sub-stiffening features. Moreover, examination of the generated buckling coefficient data illustrates the influence of skin sub-stiffening on buckling behavior, with static strength increases typically corresponding to a reduction in the number of initial skin longitudinal buckle half-waves.