3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Rotating Beams and Nonrotating Beams With Shared Eigenpair

In this paper, we look for rotating beams whose eigenpair (frequency and mode-shape) is the same as that of uniform nonrotating beams for a particular mode. It is found that, for any given mode, there exist flexural stiffness functions (FSFs) for which the jth mode eigenpair of a rotating beam, with uniform mass distribution, is identical to that of a corresponding nonrotating uniform beam with the same length and mass distribution. By putting the derived FSF in the finite element analysis of a rotating cantilever beam, the frequencies and mode-shapes of a nonrotating cantilever beam are obtained. For the first mode, a physically feasible equivalent rotating beam exists, but for higher modes, the flexural stiffness has internal singularities. Strategies for addressing the singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test-functions for rotating beam codes and for targeted destiffening of rotating beams.

A novel approach to 6-DOF adaptive trajectory tracking control of an AUV in the presence of parameter uncertainties

In this paper, the trajectory tracking control of an autonomous underwater vehicle (AUVs) in six-degrees-of-freedom (6-DOFs) is addressed. It is assumed that the system parameters are unknown and the vehicle is underactuated. An adaptive controller is proposed, based on Lyapunov׳s direct method and the back-stepping technique, which interestingly guarantees robustness against parameter uncertainties. The desired trajectory can be any sufficiently smooth bounded curve parameterized by time even if consist of straight line. In contrast with the majority of research in this field, the likelihood of actuators׳ saturation is considered and another adaptive controller is designed to overcome this problem, in which control signals are bounded using saturation functions. The nonlinear adaptive control scheme yields asymptotic convergence of the vehicle to the reference trajectory, in the presence of parametric uncertainties. The stability of the presented control laws is proved in the sense of Lyapunov theory and Barbalat׳s lemma. Efficiency of presented controller using saturation functions is verified through comparing numerical simulations of both controllers.

Estimation of gear tooth deflection by the finite element method

The finite element method (FEM) is used to determine for pitch-point, mid-point and tip loading, the deflection curve of a Image 1 diamentral pitch (DP) standard spur gear tooth corresponding to number of teeth of 14, 21, 26 and 34. In all these cases the deflection of the gear tooth at the point of loading obtained by FEM is in good agreement with the experimental value. The contraflexure in the deflection curve at the point of loading observed experimentally in the cases of pitch-point and mid-point loading, is predicted correctly by the FEM analysis.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Nonlinear transport in semiconducting polymers at high carrier densities

Conducting and semiconducting polymers are important materials in the development of printed, flexible, large-area electronics such as flat-panel displays and photovoltaic cells. There has been rapid progress in developing conjugated polymers with high transport mobility required for high-performance field-effect transistors (FETs), beginning(1) with mobilities around 10(-4) cm(2) V-1 s(-1) to a recent report(2) of 1 cm(2) V-1 s(-1) for poly(2,5-bis(3-tetradecylthiophen-2-yl) thieno[3,2-b] thiophene) (PBTTT). Here, the electrical properties of PBTTT are studied at high charge densities both as the semiconductor layer in FETs and in electrochemically doped films to determine the transport mechanism. We show that data obtained using a wide range of parameters (temperature, gate-induced carrier density, source-drain voltage and doping level) scale onto the universal curve predicted for transport in the Luttinger liquid description of the one-dimensional `metal'.

Delineating environmental envelopes to improve mapping of species distributions, via a hurdle model with CART &/or MaxEnT

Species distribution modelling (SDM) typically analyses species’ presence together with some form of absence information. Ideally absences comprise observations or are inferred from comprehensive sampling. When such information is not available, then pseudo-absences are often generated from the background locations within the study region of interest containing the presences, or else absence is implied through the comparison of presences to the whole study region, e.g. as is the case in Maximum Entropy (MaxEnt) or Poisson point process modelling. However, the choice of which absence information to include can be both challenging and highly influential on SDM predictions (e.g. Oksanen and Minchin, 2002). In practice, the use of pseudo- or implied absences often leads to an imbalance where absences far outnumber presences. This leaves analysis highly susceptible to ‘naughty-noughts’: absences that occur beyond the envelope of the species, which can exert strong influence on the model and its predictions (Austin and Meyers, 1996). Also known as ‘excess zeros’, naughty noughts can be estimated via an overall proportion in simple hurdle or mixture models (Martin et al., 2005). However, absences, especially those that occur beyond the species envelope, can often be more diverse than presences. Here we consider an extension to excess zero models. The two-staged approach first exploits the compartmentalisation provided by classification trees (CTs) (as in O’Leary, 2008) to identify multiple sources of naughty noughts and simultaneously delineate several species envelopes. Then SDMs can be fit separately within each envelope, and for this stage, we examine both CTs (as in Falk et al., 2014) and the popular MaxEnt (Elith et al., 2006). We introduce a wider range of model performance measures to improve treatment of naughty noughts in SDM. We retain an overall measure of model performance, the area under the curve (AUC) of the Receiver-Operating Curve (ROC), but focus on its constituent measures of false negative rate (FNR) and false positive rate (FPR), and how these relate to the threshold in the predicted probability of presence that delimits predicted presence from absence. We also propose error rates more relevant to users of predictions: false omission rate (FOR), the chance that a predicted absence corresponds to (and hence wastes) an observed presence, and the false discovery rate (FDR), reflecting those predicted (or potential) presences that correspond to absence. A high FDR may be desirable since it could help target future search efforts, whereas zero or low FOR is desirable since it indicates none of the (often valuable) presences have been ignored in the SDM. For illustration, we chose Bradypus variegatus, a species that has previously been published as an exemplar species for MaxEnt, proposed by Phillips et al. (2006). We used CTs to increasingly refine the species envelope, starting with the whole study region (E0), eliminating more and more potential naughty noughts (E1–E3). When combined with an SDM fit within the species envelope, the best CT SDM had similar AUC and FPR to the best MaxEnt SDM, but otherwise performed better. The FNR and FOR were greatly reduced, suggesting that CTs handle absences better. Interestingly, MaxEnt predictions showed low discriminatory performance, with the most common predicted probability of presence being in the same range (0.00-0.20) for both true absences and presences. In summary, this example shows that SDMs can be improved by introducing an initial hurdle to identify naughty noughts and partition the envelope before applying SDMs. This improvement was barely detectable via AUC and FPR yet visible in FOR, FNR, and the comparison of predicted probability of presence distribution for pres/absence.

Single layer bismuth iodide: Computational exploration of structural, electrical, mechanical and optical properties

Layered graphitic materials exhibit new intriguing electronic structure and the search for new types of two-dimensional (2D) monolayer is of importance for the fabrication of next generation miniature electronic and optoelectronic devices. By means of density functional theory (DFT) computations, we investigated in detail the structural, electronic, mechanical and optical properties of the single-layer bismuth iodide (BiI3) nanosheet. Monolayer BiI3 is dynamically stable as confirmed by the computed phonon spectrum. The cleavage energy (Ecl) and interlayer coupling strength of bulk BiI3 are comparable to the experimental values of graphite, which indicates that the exfoliation of BiI3 is highly feasible. The obtained stress-strain curve shows that the BiI3 nanosheet is a brittle material with a breaking strain of 13%. The BiI3 monolayer has an indirect band gap of 1.57 eV with spin orbit coupling (SOC), indicating its potential application for solar cells. Furthermore, the band gap of BiI3 monolayer can be modulated by biaxial strain. Most interestingly, interfacing electrically active graphene with monolayer BiI3 nanosheet leads to enhanced light absorption compared to that in pure monolayer BiI3 nanosheet, highlighting its great potential applications in photonics and photovoltaic solar cells.

Pest-damage relationships for Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) on soybean (Glycine max) and dry bean (Phaseolus vulgaris) during pod-fill.

The response of soybean (Glycine max) and dry bean (Phaseolus vulgaris) to feeding by Helicoverpa armigera during the pod-fill stage was studied in irrigated field cages over three seasons to determine the relationship between larval density and yield loss, and to develop economic injury levels. H. armigera intensity was calculated in Helicoverpa injury equivalent (HIE) units, where 1 HIE was the consumption of one larva from the start of the infestation period to pupation. In the dry bean experiment, yield loss occurred at a rate 6.00 ± 1.29 g/HIE while the rates of loss in the three soybean experiments were 4.39 ± 0.96 g/HIE, 3.70 ± 1.21 g/HIE and 2.12 ± 0.71 g/HIE. These three slopes were not statistically different (P > 0.05) and the pooled estimate of the rate of yield loss was 3.21 ± 0.55 g/HIE. The first soybean experiment also showed a split-line form of damage curve with a rate of yield loss of 26.27 ± 2.92 g/HIE beyond 8.0 HIE and a rapid decline to zero yield. In dry bean, H. armigera feeding reduced total and undamaged pod numbers by 4.10 ± 1.18 pods/HIE and 12.88 ± 1.57 pods/HIE respectively, while undamaged seed numbers were reduced by 35.64 ± 7.25 seeds/HIE. In soybean, total pod numbers were not affected by H. armigera infestation (out to 8.23 HIE in Experiment 1) but seed numbers (in Experiments 1 and 2) and the number of seeds/pod (in all experiments) were adversely affected. Seed size increased with increases in H. armigera density in two of the three soybean experiments, indicating plant compensatory responses to H. armigera feeding. Analysis of canopy pod profiles indicated that loss of pods occurred from the top of the plant downwards, but with an increase in pod numbers close to the ground at higher pest densities as the plant attempted to compensate for damage. Based on these results, the economic injury levels for H. armigera on dry bean and soybean are approximately 0.74 HIE and 2.31 HIE/m2, respectively (0.67 and 2.1 HIE/row-m for 91 cm rows).

Cellular stages of root formation, root system quality and survival of Pinus elliottii var. elliottii x P. caribaea var. hondurensis cuttings in different temperature environments.

Time to first root in cuttings varies under different environmental conditions and understanding these differences is critical for optimizing propagation of commercial forestry species. Temperature environment (15, 25, 30 or 35 +/- A 2A degrees C) had no effect on the cellular stages in root formation of the Slash x Caribbean Pine hybrid over 16 weeks as determined by histology. Initially callus cells formed in the cortex, then tracheids developed and formed primordia leading to external roots. However, speed of development followed a growth curve with the fastest development occurring at 25A degrees C and slowest at 15A degrees C with rooting percentages at week 12 of 80 and 0% respectively. Cutting survival was good in the three cooler temperature regimes (> 80%) but reduced to 59% at 35A degrees C. Root formation appeared to be dependant on the initiation of tracheids because all un-rooted cuttings had callus tissue but no tracheids, irrespective of temperature treatment and clone.

Domestication for Conservation of an Endangered Species: The Case of the Wollemi Pine

A small population of tall slender conifers was discovered in 1994 in a deep rainforest canyon of the Wollemi National Park, New SouthWales, Australia. The living trees closely resembled fossils that were more than 65 million years old, and this ‘living fossil’ was recognised as a third extant genus in the Araucariaceae (Araucaria, Agathis and now Wollemia). The species was named the Wollemi pine (W. nobilis). Extensive searches uncovered very few populations, with the total number of adult trees being less than 100. Ex situ collections were quickly established in Sydney as part of the Wollemi Pine Recovery Plan. The majority of the ex situ population was later transferred to our custom-built facility in Queensland for commercial multiplication. Domestication has relied very heavily on the species’ amenability to vegetative propagation because seed collection from the natural populations is dangerous, expensive, and undesirable for conservation reasons. Early propagation success was poor, with only about 25% of cuttings producing roots. However, small increases in propagation success have a very large impact on a domestication program because plant production can be modelled on an exponential curve where each rooted cutting develops into a mother plant that, in turn, provides more rooted cuttings. An extensive research program elevated rooting percentages to greater than 80% and also provided in vitro methods for plant multiplication. These successes have enabled international release of the Wollemi pine as a new and attractive species for ornamental horticulture.

Cellular stages of root formation, root system quality and survival of Pinuselliottii var. elliottii x P. caribaea var. hondurensis cuttings in different temperature environments.

Time to first root in cuttings varies under different environmental conditions and understanding these differences is critical for optimizing propagation of commercial forestry species. Temperature environment (15, 25, 30 or 352C) had no effect on the cellular stages in root formation of the Slash * Caribbean Pine hybrid over 16 weeks as determined by histology. Initially callus cells formed in the cortex, then tracheids developed and formed primordia leading to external roots. However, speed of development followed a growth curve with the fastest development occurring at 25C and slowest at 15C with rooting percentages at week 12 of 80 and 0% respectively. Cutting survival was good in the three cooler temperature regimes (>80%) but reduced to 59% at 35C. Root formation appeared to be dependant on the initiation of tracheids because all un-rooted cuttings had callus tissue but no tracheids, irrespective of temperature treatment and clone.

Fire resistance of light gauge steel frame wall systems lined with gypsum plasterboards

Light gauge steel frame (LSF) wall systems are increasingly used in residential and commercial buildings as load bearing and non-load bearing elements. Conventionally, the fire resistance ratings of such building elements are determined using approximate prescriptive methods based on limited standard fire tests. However, recent studies have shown that in some instances real building fire time-temperature curves could be more severe than the standard fire curve, in terms of maximum temperature and rate of temperature rise. This has caused problems for safe evacuation and rescue activities, and in some instances has also lead to the collapse of buildings earlier than the prescribed fire resistance. Therefore a detailed research study into the performance of LSF wall systems under both standard fire and realistic fire conditions was undertaken using full scale fire tests to understand the fire performance of different LSF wall configurations. Both load bearing and non-load bearing full scale fire tests were performed on LSF walls configurations which included single layer, double layer, externally insulated wall panels made up of different steel sections and thicknesses of gypsum plasterboards. The non-load bearing fire test results were utilized to understand the factors affecting the fire resistance of LSF walls, while loading bearing fire test results led to development of simplified methods to predict the fire resistance ratings of load bearing LSF walls exposed to both standard and realistic design fires. This paper presents the results of full scale experimental study and highlights the effects of standard and realistic fire conditions on fire performance of LSF walls.

Fatigue capacity of cold-formed steel roof battens under cyclic wind uplift loads

Steel roofs made of thin cold-formed steel roof claddings and battens are widely used in low-rise residential and industrial buildings all around the world. However, they suffer from premature localised pull-through failures in the batten to rafter connections during high wind events. A recent study proposed a suitable design equation for the pull-through failures of thin steel roof battens. However, it was limited to static wind uplift loading. In contrast, most cyclone/storm events produce cyclic wind uplift forces on roofs for a significantly long period, thus causing premature fatigue pull-through failures at lower loads. Therefore, a series of constant amplitude cyclic load tests was conducted on small and full scale roof panels made of a commonly used industrial roof batten to develop their S-N curves. A series of multi-level cyclic tests, including the recently introduced low-high-low (LHL) fatigue loading test, was also undertaken to simulate a design cyclone. Using the S-N curves, the static pull-through design capacity equation was modified to include the effects of fatigue. Applicability of Miner’s rule was evaluated in order to predict the fatigue damage caused by multi-level cyclic tests such as the LHL test, and suitable modifications were made. The combined use of the modified Miner’s law and the S-N curve of roof battens will allow a conservative estimation of the fatigue design capacity of roof battens without conducting the LHL tests simulating a design cyclone. This paper presents the details of this study, and the results.

Early detection of type 2 diabetes mellitus in Chinese and Indian adult population

Objectives of this study were to determine secular trends of diabetes prevalence in China and develop simple risk assessment algorithms for screening individuals with high-risk for diabetes or with undiagnosed diabetes in Chinese and Indian adults. Two consecutive population based surveys in Chinese and a prospective study in Mauritian Indians were involved in this study. The Chinese surveys were conducted in randomly selected populations aged 20-74 years in 2001-2002 (n=14 592) and 35-74 years in 2006 (n=4416). A two-step screening strategy using fasting capillary plasma glucose (FCG) as first-line screening test followed by standard 2-hour 75g oral glucose tolerance tests (OGTTs) was applied to 12 436 individuals in 2001, while OGTTs were administrated to all participants together with FCG in 2006 and to 2156 subjects in 2002. In Mauritius, two consecutive population based surveys were conducted in Mauritian Indians aged 20-65 years in 1987 and 1992; 3094 Indians (1141 men), who were not diagnosed as diabetes at baseline, were reexamined with OGTTs in 1992 and/or 1998. Diabetes and pre-diabetes was defined following 2006 World Health Organization/ International Diabetes Federation Criteria. Age-standardized, as well as age- and sex-specific, prevalence of diabetes and pre-diabetes in adult Chinese was significantly increased from 12.2% and 15.4% in 2001 to 16.0% and 21.2% in 2006, respectively. A simple Chinese diabetes risk score was developed based on the data of Chinese survey 2001-2002 and validated in the population of survey 2006. The risk scores based on β coefficients derived from the final Logistic regression model ranged from 3 – 32. When the score was applied to the population of survey 2006, the area under operating characteristic curve (AUC) of the score for screening undiagnosed diabetes was 0.67 (95% CI, 0.65-0.70), which was lower than the AUC of FCG (0.76 [0.74-0.79]), but similar to that of HbA1c (0.68 [0.65-0.71]). At a cut-off point of 14, the sensitivity and specificity of the risk score in screening undiagnosed diabetes was 0.84 (0.81-0.88) and 0.40 (0.38-0.41). In Mauritian Indian, body mass index (BMI), waist girth, family history of diabetes (FH), and glucose was confirmed to be independent risk predictors for developing diabetes. Predicted probabilities for developing diabetes derived from a simple Cox regression model fitted with sex, FH, BMI and waist girth ranged from 0.05 to 0.64 in men and 0.03 to 0.49 in women. To predict the onset of diabetes, the AUC of the predicted probabilities was 0.62 (95% CI, 0.56-0.68) in men and 0.64(0.59-0.69) in women. At a cut-off point of 0.12, the sensitivity and specificity was 0.72(0.71-0.74) and 0.47(0.45-0.49) in men; and 0.77(0.75-0.78) and 0.50(0.48-0.52) in women, respectively. In conclusion, there was a rapid increase in prevalence of diabetes in Chinese adults from 2001 to 2006. The simple risk assessment algorithms based on age, obesity and family history of diabetes showed a moderate discrimination of diabetes from non-diabetes, which may be used as first line screening tool for diabetes and pre-diabetes, and for health promotion purpose in Chinese and Indians.