Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Tree growth relationships and silvicultural tools to assist stand management in private native spotted gum dominant forests in Queensland and northern New South Wales.

Spotted gum dominant forests occur from Cooktown in northern Queensland (Qld) to Orbost in Victoria (Boland et al. 2006) and these forests are commercially very important with spotted gum the most commonly harvested hardwood timber in Qld and one of the most important in New South Wales (NSW). Spotted gum has a wide range of end uses from solid wood products through to power transmission poles and generally has excellent sawing and timber qualities (Hopewell 2004). The private native forest resource in southern Qld and northern NSW is a critical component of the hardwood timber industry (Anon 2005, Timber Qld 2006) and currently half or more of the native forest timber resource harvested in northern NSW and Qld is sourced from private land. However, in many cases productivity on private lands is well below what could be achieved with appropriate silvicultural management. This project provides silvicultural management tools to assist extension staff, land owners and managers in the south east Qld and north eastern NSW regions. The intent was that this would lead to improvement of the productivity of the private estate through implementation of appropriate management. The other intention of this project was to implement a number of silvicultural experiments and demonstration sites to provide data on growth rates of managed and unmanaged forests so that landholders can make informed decisions on the future management of their forests. To assist forest managers and improve the ability to predict forest productivity in the private resource, the project has developed: • A set of spotted gum specific silvicultural guidelines for timber production on private land that cover both silvicultural treatment and harvesting. The guidelines were developed for extension officers and property owners. • A simple decision support tool, referred to as the spotted gum productivity assessment tool (SPAT), that allows an estimation of: 1. Tree growth productivity on specific sites. Estimation is based on the analysis of site and growth data collected from a large number of yield and experimental plots on Crown land across a wide range of spotted gum forest types. Growth algorithms were developed using tree growth and site data and the algorithms were used to formulate basic economic predictors. 2. Pasture development under a range of tree stockings and the expected livestock carrying capacity at nominated tree stockings for a particular area. 3. Above-ground tree biomass and carbon stored in trees. •A series of experiments in spotted gum forests on private lands across the study area to quantify growth and to provide measures of the effect of silvicultural thinning and different agro-forestry regimes. The adoption and use of these tools by farm forestry extension officers and private land holders in both field operations and in training exercises will, over time, improve the commercial management of spotted gum forests for both timber and grazing. Future measurement of the experimental sites at ages five, 10 and 15 years will provide longer term data on the effects of various stocking rates and thinning regimes and facilitate modification and improvement of these silvicultural prescriptions.

On the kinetics of crystal growth from a supercooled melt

We present a theoretical analysis of the dynamics of crystal growth from a supercooled melt. A molecular theory of crystal growth that pays proper attention to the structure at the liquid-solid interface is discussed.

Seed production of Stylosanthes guyanensis. 1. Growth and development.

The pattern of growth and development of seed crops of stylo (Stylosanthes guyanensis) was derived from measurements made on experimental and commercial crops in north Queensland. The three cultivars Cook, Endeavour, and Schofield differed appreciably only in the timetable of their development. Each had distinct successive phases of vegetative and reproductive development culminating in total annual seed production of 700-800 kg ha-1 from a healthy closed canopy, the main recorded cause of reduced production being the disease Botrytis sp. In a healthy crop of Cook, the peak quantity of standing seed represented almost 90 per cent of the total accountable seed, and the rise to and decline from this peak proceeded at rates of the order of 3-4 per cent per day. It is deduced that, although there appears to be little potential for either increase in overall production or improvement in synchronization or retention characteristics beyond that currently attained by a closed canopy of healthy plants, there is scope for an increase in the efficiency of recovery of standing seed. Maximum recovery will be achieved through attention to choice of time of harvest, presentation of a minimum amount of extraneous vegetation to the harvester, and improvement in harvester separation.

Effects of stage of defoliation on seed production and growth of Stylosanthes humilis.

Stylosanthes humilis swards grown at Brisbane in irrigated boxes were defoliated (about 60 per cent removal of tops) at floral initiation, first flower appearance, or advanced flowering stages ; seed yield was 45, 16, and 14 per cent respectively of seed yield in undefoliated swards. Decreased yields were primarily due to poor seed set of florets, were also associated with reduced inflorescence density and floret number per inflorescence, and occurred despite increases (in some defoliation treatments) in seed size, leaf growth rate, and differentiation of leaves and branches. Total seasonal plant growth was independent of defoliation treatment.

Effects of secondary crops on bacterial growth and nitrogen removal in shrimp farm effluent treatment systems

Secondary crops provide a means of assimilating some effluent nitrogen from eutrophic shrimp farm settlement ponds. However, a more important role may be their stimulation of beneficial bacterial nitrogen removal processes. In this study, bacterial biomass, growth and nitrogen removal capacity were quantified in shrimp farm effluent treatment systems containing vertical artificial substrates and either the banana shrimp Penaeus merguiensis (de Man) or the grey mullet, Mugil cephalus L. Banana shrimp were found to actively graze biofilm on the artificial substrates and significantly reduced bacterial biomass relative to a control (24.5 ± 5.6mgCm−2 and 39.2 ± 8.7mgCm−2, respectively). Bacterial volumetric growth rates, however, were significantly increased in the presence of the shrimp relative to the control 45.2±11.3mgCm−2 per day and 22.0±4.3mgCm−2 per day, respectively). Specific growth rate, or growth rate per cell, of bacteria was therefore appreciably stimulated by the banana shrimp. Nitrate assimilation was found to be significantly higher on grazed substrate biofilm relative to the control (223±54 mgNm−2 per day and 126±36 mg Nm−2 per day, respectively), suggesting that increased bacterial growth rate does relate to enhanced nitrogen uptake. Regulated banana shrimp feeding activity therefore can increase the rate of newbacterial biomass production and also the capacity for bacterial effluent nitrogen assimilation. Mullet had a negligible influence on the biofilm associated with the artificial substrate but reduced sediment bacterial biomass (224 ± 92 mgCm−2) relative to undisturbed sediment (650 ± 254 mgCm−2). Net, or volumetric bacterial growth in the sediment was similar in treatments with and without mullet, suggesting that the growth rate per cell of bacteria in grazed sediments was enhanced. Similar rates of dissolved nitrogen mineralisation werefound in sediments with and without mullet but nitrificationwas reduced. Presence of mullet increased water column suspended solids concentrations, water column bacterial growth and dissolved nutrient uptake. This study has shown that secondary crops, particularly banana shrimp, can play a stimulatory role in the bacterial processing of effluent nitrogen in eutrophic shrimp effluent treatment systems.

Strategies to increase growth of the weaned Bali calf

R&D to increase growth of Bali calves in the Eastern Islands of Indonesia.

Optimising growth paths of beef cattle in northern Australia for increased profit

Strategies for increasing growth of cattle using different growth paths.

Spore and crystal formation in Bacillus thuringiensis var thuringiensis during growth in cystine and cysteine.

The effect of the addition of different concentratons of cystine and cysteine on sporulation and parasporal crystal formation in Bacillus thuringiensis var. thuringiensis was studied. The effect was well pronounced when the systine/cysteine additions were made after the stationary phase. Heat stable spores and crystals were formed when the culture was provided with a low concentration of cystine/cysteine (0.05 per cent w/v). At a moderate concentration of cystine or cysteine (0.15%), only heat labile spores were formed without the production of the crystal. When the cystine/cysteine concentration was high (0.25%), spore and crystal formation were completely inhibited. Partial reversal of inhibition of sporulation was brought about by sodium sulphate or zinc sulphate and lead, copper, cadmium or cobalt acetate at 0.2 mM or at 0.2% of sodium or potassium pyruvate, citrate, isaconitate, oxalosuccinate, ∝ -keto-glutarate, succinate, fumarate, malate, or oxalacetate. Glutamate (0.2%) overcame the inhibitory effect of cystine/cysteine completely. The structural changes observed using phase contrast microscopy were dependent upon the concentration of cystine/cysteine.

Growth of Mycobacterium smegmatis in minimal and complete media

The growth patterns of Mycobacterium smegmatis SN2 in a minimal medium and in nutrient broth have been compared. The growth was monitored by absorbancy (Klett readings), colony forming units, wet weight and content of DNA, RNA and protein. During the early part of the growth cycle, the bacteria had higher wet weight and macromolecular content in nutrient broth than in minimal media. During the latter half of the growth cycle however, biosynthesis stopped much earlier in nutrient broth and the bacteria had a much lower content of macromolecules than in the minimal medium. In both the media, a general pattern of completing biosynthesis rapidly in the initial phase and a certain amount of cell division at a later time involving the distribution of preformed macromolecules was seen. The possible adaptive significance of this observation has been discussed.