Photochemical reactions of organic crystals

Abstract is not available.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Avocado 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 2001. We advise readers to take particular note of the areas most likely to be out-of-date and so requiring further research: see detailed reprint 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 2001. 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 avocadoes. 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.

Papaw 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 http://www.deedi.qld.gov.au/ (Select: Queenslands 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 the production of papaw. 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.

Mango 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 1999. 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 mangoes. 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.

Citrus 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 citrus. 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.

Rockmelon and Honeydew 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 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 Rockmelon and Honeydew. 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.

Capsicum and Chilli 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 1999. 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 capsicum and chilli. 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.

Cashew 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 1999. 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 cashews. 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.

Custard Apple 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 1998. 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 custard apples. 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.

Strawberry 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 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 strawberries. 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.

Tomato 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 1998. 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 Tomatoes. 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.

Tropical 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 1998.. 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 tropical 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.