A note on the period of oscillation of non-linear systems

This paper deals with two approximate methods of finding the period of oscillations of non-linear conservative systems excited by step functions. The first method is an extension of the analysis presented by Jonckheere [4] and the second one is based on a weighted bilinear approximation of the non-linear characteristic. An example is presented and the approximate results are compared with the exact results

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Targeting resource investments to achieve sediment reduction and improved Great Barrier Reef health

Concerns about excessive sediment loads entering the Great Barrier Reef (GBR) lagoon in Australia have led to a focus on improving ground cover in grazing lands. Ground cover has been identified as an important factor in reducing sediment loads, but improving ground cover has been difficult for reef stakeholders in major catchments of the GBR. To provide better information an optimising linear programming model based on paddock scale information in conjunction with land type mapping was developed for the Fitzroy, the largest of the GBR catchments. This identifies at a catchment scale which land types allow the most sediment reduction to be achieved at least cost. The results suggest that from the five land types modelled, the lower productivity land types present the cheapest option for sediment reductions. The study allows more informed decision making for natural resource management organisations to target investments. The analysis highlights the importance of efficient allocation of natural resource management funds in achieving sediment reductions through targeted land type investments. © 2012.

Wheat biomass and yield increased when populations of the root-lesion nematode (Pratylenchus thornei) were reduced through sequential rotation of partially resistant winter and summer crops

The root-lesion nematode, Pratylenchus thornei, can reduce wheat yields by >50%. Although this nematode has a broad host range, crop rotation can be an effective tool for its management if the host status of crops and cultivars is known. The summer crops grown in the northern grain region of Australia are poorly characterised for their resistance to P. thornei and their role in crop sequencing to improve wheat yields. In a 4-year field experiment, we prepared plots with high or low populations of P. thornei by growing susceptible wheat or partially resistant canaryseed (Phalaris canariensis); after an 11-month, weed-free fallow, several cultivars of eight summer crops were grown. Following another 15-month, weed-free fallow, P. thornei-intolerant wheat cv. Strzelecki was grown. Populations of P. thornei were determined to 150 cm soil depth throughout the experiment. When two partially resistant crops were grown in succession, e.g. canaryseed followed by panicum (Setaria italica), P. thornei populations were <739/kg soil and subsequent wheat yields were 3245 kg/ha. In contrast, after two susceptible crops, e.g. wheat followed by soybean, P. thornei populations were 10 850/kg soil and subsequent wheat yields were just 1383 kg/ha. Regression analysis showed a linear, negative response of wheat biomass and grain yield with increasing P. thornei populations and a predicted loss of 77% for biomass and 62% for grain yield. The best predictor of wheat yield loss was P. thornei populations at 0-90 cm soil depth. Crop rotation can be used to reduce P. thornei populations and increase wheat yield, with greatest gains being made following two partially resistant crops grown sequentially.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

The effect of pasture utilization rate on stocks of soil organic carbon and total nitrogen in a semi-arid tropical grassland

The influence of grazing management on total soil organic carbon (SOC) and soil total nitrogen (TN) in tropical grasslands is an issue of considerable ecological and economic interest. Here we have used linear mixed models to investigate the effect of grazing management on stocks of SOC and TN in the top 0.5 m of the soil profile. The study site was a long-term pasture utilization experiment, 26 years after the experiment was established for sheep grazing on native Mitchell grass (Astrebla spp.) pasture in northern Australia. The pasture utilization rates were between 0% (exclosure) and 80%, assessed visually. We found that a significant amount of TN had been lost from the top 0.1 m of the soil profile as a result of grazing, with 80% pasture utilization resulting in a loss of 84 kg ha−1 over the 26-year period. There was no significant effect of pasture utilization rate on TN when greater soil depths were considered. There was no significant effect of pasture utilization rate on stocks of SOC and soil particulate organic carbon (POC), or the C:N ratio at any depth; however, visual trends in the data suggested some agreement with the literature, whereby increased grazing pressure appeared to: (i) decrease SOC and POC stocks; and, (ii) increase the C:N ratio. Overall, the statistical power of the study was limited, and future research would benefit from a more comprehensive sampling scheme. Previous studies at the site have found that a pasture utilization rate of 30% is sustainable for grazing production on Mitchell grass; however, given our results, we conclude that N inputs (possibly through management of native N2-fixing pasture legumes) should be made for long-term maintenance of soil health, and pasture productivity, within this ecosystem.

Preparation of Industrially Important Hydroxy Acids and Diacids from 2,2-Disubstituted Propane-1,3-Diols and Linear Primary Diols by Green Chemistry Methods

Environmentally benign and economical methods for the preparation of industrially important hydroxy acids and diacids were developed. The carboxylic acids, used in polyesters, alkyd resins, and polyamides, were obtained by the oxidation of the corresponding alcohols with hydrogen peroxide or air catalyzed by sodium tungstate or supported noble metals. These oxidations were carried out using water as a solvent. The alcohols are also a useful alternative to the conventional reactants, hydroxyaldehydes and cycloalkanes. The oxidation of 2,2-disubstituted propane-1,3-diols with hydrogen peroxide catalyzed by sodium tungstate afforded 2,2-disubstituted 3-hydroxypropanoic acids and 1,1-disubstituted ethane-1,2-diols as products. A computational study of the Baeyer-Villiger rearrangement of the intermediate 2,2-disubstituted 3-hydroxypropanals gave in-depth data of the mechanism of the reaction. Linear primary diols having chain length of at least six carbons were easily oxidized with hydrogen peroxide to linear dicarboxylic acids catalyzed by sodium tungstate. The Pt/C catalyzed air oxidation of 2,2-disubstituted propane-1,3-diols and linear primary diols afforded the highest yield of the corresponding hydroxy acids, while the Pt, Bi/C catalyzed oxidation of the diols afforded the highest yield of the corresponding diacids. The mechanism of the promoted oxidation was best described by the ensemble effect, and by the formation of a complex of the hydroxy and the carboxy groups of the hydroxy acids with bismuth atoms. The Pt, Bi/C catalyzed air oxidation of 2-substituted 2-hydroxymethylpropane-1,3-diols gave 2-substituted malonic acids by the decarboxylation of the corresponding triacids. Activated carbon was the best support and bismuth the most efficient promoter in the air oxidation of 2,2-dialkylpropane-1,3-diols to diacids. In oxidations carried out in organic solvents barium sulfate could be a valuable alternative to activated carbon as a non-flammable support. In the Pt/C catalyzed air oxidation of 2,2-disubstituted propane-1,3-diols to 2,2-disubstituted 3-hydroxypropanoic acids the small size of the 2-substituents enhanced the rate of the oxidation. When the potential of platinum of the catalyst was not controlled, the highest yield of the diacids in the Pt, Bi/C catalyzed air oxidation of 2,2-dialkylpropane-1,3-diols was obtained in the regime of mass transfer. The most favorable pH of the reaction mixture of the promoted oxidation was 10. The reaction temperature of 40°C prevented the decarboxylation of the diacids.

The kinetics and reactivity of several polyatomic free radicals in reactions with NO2, O2, Cl2, and HCl

In this thesis, the kinetics of several alkyl, halogenated alkyl, and alkenyl free radical reactions with NO2, O2, Cl2, and HCl reactants were studied over a wide temperature range in time resolved conditions. Laser photolysis photoionisation mass spectrometer coupled to a flow reactor was the experimental method employed and this thesis present the first measurements performed with the experimental system constructed. During this thesis a great amount of work was devoted to the designing, building, testing, and improving the experimental apparatus. Carbon-centred free radicals were generated by the pulsed 193 or 248 nm photolysis of suitable precursors along the tubular reactor. The kinetics was studied under pseudo-first-order conditions using either He or N2 buffer gas. The temperature and pressure ranges employed were between 190 and 500 K, and 0.5 45 torr, respectively. The possible role of heterogeneous wall reactions was investigated employing reactor tubes with different sizes, i.e. to significantly vary the surface to volume ratio. In this thesis, significant new contributions to the kinetics of carbon-centred free radical reactions with nitrogen dioxide were obtained. Altogether eight substituted alkyl (CH2Cl, CHCl2, CCl3, CH2I, CH2Br, CHBr2, CHBrCl, and CHBrCH3) and two alkenyl (C2H3, C3H3) free radical reactions with NO2 were investigated as a function of temperature. The bimolecular rate coefficients of all these reactions were observed to possess negative temperature dependencies, while pressure dependencies were not noticed for any of these reactions. Halogen substitution was observed to moderately reduce the reactivity of substituted alkyl radicals in the reaction with NO2, while the resonance stabilisation of the alkenyl radical lowers its reactivity with respect to NO2 only slightly. Two reactions relevant to atmospheric chemistry, CH2Br + O2 and CH2I + O2, were also investigated. It was noticed that while CH2Br + O2 reaction shows pronounced pressure dependence, characteristic of peroxy radical formation, no such dependence was observed for the CH2I + O2 reaction. Observed primary products of the CH2I + O2 reaction were the I-atom and the IO radical. Kinetics of CH3 + HCl, CD3 + HCl, CH3 + DCl, and CD3 + DCl reactions were also studied. While all these reactions possess positive activation energies, in contrast to the other systems investigated in this thesis, the CH3 + HCl and CD3 + HCl reactions show a non-linear temperature dependency on the Arrhenius plot. The reactivity of substituted methyl radicals toward NO2 was observed to increase with decreasing electron affinity of the radical. The same trend was observed for the reactions of substituted methyl radicals with Cl2. It is proposed that interactions of frontier orbitals are responsible to these observations and Frontier Orbital Theory could be used to explain the observed reactivity trends of these highly exothermic reactions having reactant-like transition states.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Developing effective fumigation protocols to manage strongly phosphine-resistant Cryptolestes ferrugineus (Stephens) (Coleoptera: Laemophloeidae)

BACKGROUND The emergence of high levels of resistance in Cryptolestes ferrugineus (Stephens) in recent years threatens the sustainability of phosphine, a key fumigant used worldwide to disinfest stored grain. We aimed at developing robust fumigation protocols that could be used in a range of practical situations to control this resistant pest. RESULTS Values of the lethal time to kill 99.9% (LT99.9, in days) of mixed-age populations, containing all life stages, of a susceptible and a strongly resistant C. ferrugineus population were established at three phosphine concentrations (1.0, 1.5 and 2.0 mg L−1) and three temperatures (25, 30 and 35 °C). Multiple linear regression analysis revealed that phosphine concentration and temperature both contributed significantly to the LT99.9 of a population (P < 0.003, R2 = 0.92), with concentration being the dominant variable, accounting for 75.9% of the variation. Across all concentrations, LT99.9 of the strongly resistant C. ferrugineus population was longest at the lowest temperature and shortest at the highest temperature. For example, 1.0 mg L−1 of phosphine is required for 20, 15 and 15 days, 1.5 mg L−1 for 12, 11 and 9 days and 2.0 mg L−1 for 10, 7 and 6 days at 25, 30 and 35 °C, respectively, to achieve 99.9% mortality of the strongly resistant C. ferrugineus population. We also observed that phosphine concentration is inversely proportional to fumigation period in regard to the population extinction of this pest. CONCLUSION The fumigation protocols developed in this study will be used in recommending changes to the currently registered rates of phosphine in Australia towards management of strongly resistant C. ferrugineus populations, and can be repeated in any country where this type of resistance appears.

Estimates of genetic parameters for growth and wood properties in Eucalyptus pellita F. Muell. to support tree breeding in Vietnam

Key message Eucalyptus pellita demonstrated good growth and wood quality traits in this study, with young plantation grown timber being suitable for both solid and pulp wood products. All traits examined were under moderate levels of genetic control with little genotype by environment interaction when grown on two contrasting sites in Vietnam. Context Eucalyptus pellita currently has a significant role in reforestation in the tropics. Research to support expanded of use of this species is needed: particularly, research to better understand the genetic control of key traits will facilitate the development of genetically improved planting stock. Aims This study aimed to provide estimates of the heritability of diameter at breast height over bark, wood basic density, Kraft pulp yield, modulus of elasticity and microfibril angle, and the genetic correlations among these traits, and understand the importance of genotype by environment interactions in Vietnam. Methods Data for diameter and wood properties were collected from two 10-year-old, open-pollinated progeny trials of E. pellita in Vietnam that evaluated 104 families from six native range and three orchard sources. Wood properties were estimated from wood samples using near-infrared (NIR) spectroscopy. Data were analysed using mixed linear models to estimate genetic parameters (heritability, proportion of variance between seed sources and genetic correlations). Results Variation among the nine sources was small compared to additive variance. Narrow-sense heritability and genetic correlation estimates indicated that simultaneous improvements in most traits could be achieved from selection among and within families as the genetic correlations among traits were either favourable or close to zero. Type B genetic correlations approached one for all traits suggesting that genotype by environment interactions were of little importance. These results support a breeding strategy utilizing a single breeding population advanced by selecting the best individuals across all seed sources. Conclusion Both growth and wood properties have been evaluated. Multi-trait selection for growth and wood property traits will lead to more productive populations of E. pellita both with improved productivity and improved timber and pulp properties.

Infrared spectroscopy as a rapid tool to detect methylglyoxal and antibacterial activity in Australian honeys

Methylglyoxal (2-oxopropanal) is a compound known to contribute to the non-peroxide antimicrobial activity of honeys. The feasibility of using infrared spectroscopy as a predictive tool for honey antibacterial activity and methylglyoxal content was assessed. A linear relationship was found between methylglyoxal content (279–1755 mg/kg) in Leptospermum polygalifolium honeys and bacterial inhibition for Escherichiacoli (R2 = 0.80) and Staphylococcusaureus (R2 = 0.64). A good prediction of methylglyoxal (R2 0.75) content in honey was achieved using spectroscopic data from the mid infrared (MIR) range in combination with partial least squares regression. These results indicate that robust predictive equations could be developed using MIR for commercial application where the prediction of bacterial inhibition is needed to ‘value’ honeys with methylglyoxal contents in excess of 200 mg/kg.

Comments on a decentralized control of linear multivariable systems

A strongly connected decentralized control system may be made single channel controllable and observable with respect to any channel by decentralized feedbacks. It is noted here that the system example considered by Corfmat and Morse to illustrate this fact is already single channel controllable and observable, with respect to one of the channels. An alternate example which fits into the situation is presented in this item.