Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0growing domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

Sweet Potato Information Kit. Agrilink, your growing guide to better farming guide.

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 1999. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1998. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of low chill stonefruit. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Wine Grape Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.daf.qld.gov.au. This publication has been reprinted as a digital book without any changes to the content published in 1997. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 1997. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of wine grape. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Fruit traits of vertebrate-dispersed alien plants: smaller seeds and more pulp sugar than indigenous species

Vertebrates play a major role in dispersing seeds of fleshy-fruited alien plants. However, we know little of how the traits of alien fleshy fruits compare with indigenous fleshy fruits, and how these differences might contribute to invasion success. In this study, we characterised up to 38 fruit morphology, pulp nutrient and phenology traits of an assemblage of 34 vertebrate-dispersed alien species in south-eastern Queensland, Australia. Most alien fruits were small (81%\15 mm in mean width), and had watery fruit pulps that were high in sugars and low in nitrogen and lipids. When compared to indigenous species, alien fruits had significantly smaller seeds. Further, alien fruit pulps contained more sugar and more variable (and probably greater) nitrogen per pulp wet weight, and species tended to have longer fruiting seasons than indigenous species. Our analyses suggest that fruit traits could be important in determining invasiveness and could be used to improve pre- and post-border weed risk assessment.

Premature fruit softening, a major physiological problem of persimmon in subtropical Australia.

Premature or abnormal softening of persimmon fruit within 3-7 days after harvest is a major physiological problem of non-astringent persimmon cultivars grown in subtropical regions of Australia. Up to 30% of consignments may soften rapidly frequently overnight, often resulting in the flesh becoming very soft, completely translucent, and impossible to handle. Incidence of premature soft fruit can vary with season and production location. To study the incidence of this problem, we conducted surveys of fruit harvested from five environmentally-diverse regions of Australia over a two-year period. We found wide variation in the rate of both premature softening and normal softening with differences of up 37 days between orchards in percentage of fruit reaching 50% soft. We found that the rate of fruit softening was exacerbated by lower calcium concentrations at fruit set, shorter fruit development periods and heavier rainfall during the fruit development period. The implications of our findings, in terms of orchard management, export and domestic marketing strategies are discussed.

Timing of infection of macadamia fruit by Pseudocercospora macadamiae and climatic effects on growth and spore germination.

Pseudocercospora macadamiae causes husk spot of macadamia. Husk spot control would be improved by verifying the stages in fruit development susceptible to infection, and determine some of the climatic conditions likely to lead to high disease pressure periods in the field. Our results showed that the percent conidia germination and growth of germ tubes and mycelia of P. macadamiae were greatest at 26 degrees C, with better conidia germination associated with high relative humidity and free water. The exposure of match-head-sized and pea-sized fruit stages to natural P. macadamiae inoculum in the field led to 2 5-fold increases in husk spot incidence, and up to 8.5-fold increases in premature abscission, compared with unexposed fruit. Exposure of fruit stages later than match-head-sized and pea-sized fruit generally caused no further increases in disease incidence or premature abscission. Climatic conditions were found to have a strong influence on the behaviour of P. macadamiae, the host, oil accumulation, and the subsequent impact of husk spot on premature abscission. Our findings suggest that fungicide application should target fruit at the match-head-sized stage of development in order to best reduce yield losses, particularly in seasons where oil accumulation in fruit is prolonged and climatic conditions are optimal for P. macadamiae.

The use of heat-sums to predict harvest dates following potassium chlorate (KClO3) application in longan.

The ability to initiate and manipulate flowering with KClO3 allows flowering of longan, to be triggered outside of the normal flowering season (July-September) in Australia. Fruit maturity following normal flowering will occur approximately six-eight months (180-220 days) from flowering, depending on variety. Out of season flowering will result in differing times to maturity due to different temperature regimes during the maturity period. Knowing how long fruit will take to mature from different KClO3 application dates is potentially a valuable tool for growers to use as it would allow them to time their applications with market opportunities, e.g. Chinese New Year, periods of low volumes or periods of high prices. A simple heat-sum calculation was shown to reliably quantify fruit maturity periods, 2902 and 3432 growing degree days for Kohala and Biew Kiew respectively. Growers can use heat-sum as a predictive tool to allow for efficient planning of harvesting, packaging and freight requirements.

The effect of foliar sprays of the synthetic auxin 3-5-6 TPA, on fruit drop, fruit size and seed development in three lychee (Litchi chinensis) cultivars: Tai So, Fay Zee Sui and Kwai Mai Pink.

Fruit drop in lychee can cause major yield losses in Australia, the severity varying with cultivar and season. Research in China, South Africa and Israel has demonstrated the potential for synthetic auxins used as foliar sprays to reduce fruit drop in lychee. Trials were initiated in Australia to test the efficacy of the synthetic auxin, 3-5-6 Trichloro-2-phridyl-oxyacetic acid (3-5-6 TPA) at 50 ppm on the cultivars Tai So, Fay Zee Sui and Kwai Mai Pink. Results indicate that in most cases the TPA reduced natural fruit drop however the size of the fruit at the time of application affects the response and the ideal application time varies with cultivar; approximately 13 mm fruit length in 'Kwai Mai Pink', 20 mm in 'Fay Zee Sui' and 27 mm in 'Tai So'. If applied too early in 'Tai So', it caused an increase in fruit drop. The TPA was most effective when natural fruit drop was high, reducing fruit drop from 74.7 to 34.9% in 'Kwai Mai Pink' and least effective when natural fruit drop was low. An increase in the percentage of fruit with poorly developed (chicken tongue) seed and slightly larger fruit size was also observed in treated trees.

Macadamia Information Kit. Agrilink, your growing guide to better farming guide

ABSTRACT: Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in macadamia grower's handbook. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2004. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of macadamias. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Brassica Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 2004. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2004. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of brassica. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Subtropical Banana Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 2004. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2004. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of subtropical bananas. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Sweet Corn Information Kit. Agrilink, your growing guide to better farming guide

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.deedi.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 2005. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2005. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in the production of sweet corn. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Growing banana prawns in prawn farm settlement ponds to utilise and help remove waste nutrients.

To assess their utility for profitable wastewater bioremediation, banana prawns, Penaeus (Fenneropenaeus) merguiensis (de Man), were stocked at low densities (1 – 5 m-2) and grown without supplemental feeding in five commercial-prawn-farm settlement ponds (0.3 to 6.0 ha). The prawns free-ranged in the variously designed ponds for 160 to 212 days after stocking as PL15. Survival estimates ranged from 12% to 60% with production of 50 – 528 kg ha-1. Over 1150 kg of marketable product was produced in the study. Exceptional growth was monitored at one farm where prawns reached an average size of 17g in 80 days. Nutrients in water flowing into (8 - 40 ML d-1) and out of the settlement pond at that farm were assessed twice weekly along with routine water quality measurements. Only small differences in water qualities were detected between waters running into and out of this settlement pond. Total nitrogen levels gradually increased from 1 - 1.5 mg L-1 early in the season to over 3 mg L-1 towards the end of the season. Total phosphorus levels similarly rose from 0.1 - 0.2 mg L-1 to 0.3 - 0.4 mg L-1 in the middle of the season, but fell to 0.2 – 0.3 mg L-1 towards the end when approximately 12,000 prawns were harvested with a total weight of 175 kg. No significant differences (P > 0.05) were detected in the overall acceptability of prawns harvested from each of the 5 settlement ponds in small-scale consumer sensory analyses. The prawns from settlement ponds were rated similarly to banana prawns grown with commercial diets at two other establishments. Microbiological analyses of prawns from all farms showed bacterial levels to be well within food-grade standards and lower than prawns produced in a normal growout pond. These results demonstrate that high quality food grade banana prawns can be produced in these wastewater treatment systems.

Integrated Pest Management in Ornamentals: Information Guide. Horticulture Series: Agrilink,your growing guide to better farming.

Each Agrilink kit has been designed to be both comprehensive and practical. As the kits are arranged to answer questions of increasing complexity, they are useful references for both new and experienced producers of specific crops. Agrilink integrates the technology of horticultural production with the management of horticultural enterprises. REPRINT INFORMATION - PLEASE READ! For updated information please call 13 25 23 or visit the website www.daff.qld.gov.au (Select: Queensland Industries – Agriculture link) This publication has been reprinted as a digital book without any changes to the content published in 2000. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed information on first page of the kit. Even with these limitations we believe this information kit provides important and valuable information for intending and existing growers. This publication was last revised in 2000. The information is not current and the accuracy of the information cannot be guaranteed by the State of Queensland. This information has been made available to assist users to identify issues involved in integrated pest management in ornamentals. This information is not to be used or relied upon by users for any purpose which may expose the user or any other person to loss or damage. Users should conduct their own inquiries and rely on their own independent professional advice. While every care has been taken in preparing this publication, the State of Queensland accepts no responsibility for decisions or actions taken as a result of any data, information, statement or advice, expressed or implied, contained in this publication.

Sustaining and Growing Landcare Systems in the Philippines and Australia

Sustaining and Growing Landcare Systems in the Philippines and Australia.