My Trip to Notan

My Trip to Notan charts my own journey from the rawness and acceptance of multiple life losses into understanding, and finally, renewal. The key result of this project is a prototype book, a 48-page digital Print-On-Demand (POD) publication, which also includes a DVD that inserts into book’s back and features live demonstrations, interviews and other segments related to the book. Additionally, the body of work from which the book was gleaned was presented at the thesis exhibition. Ultimately, My Trip to Notan is a sketch of my understanding of the framework that threads through design, physics and philosophy, inspired by the simplicity of the ancient art of Notan, and upon my own fragmentary observations gathered from the journey. My hope was to reveal some sense of the pulse that drives the inquiry, rather than the suggestion of any sort of destination

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics

Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about \emph{arbitrary}, far-from equilibrium reference states. The primary result is a set of hydrodynamic equations for studying variations from the arbitrary reference state which, unlike the usual Navier-Stokes hydrodynamics, does not restrict the reference state in any way. The method is illustrated by application to a sheared granular gas which cannot be studied using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc. errors Replaced to correct misc. errors, make notation more consistant, extend discussio

Enskog Theory for Polydisperse Granular Mixtures II. Sonine Polynomial Approximation

The linear integral equations defining the Navier-Stokes (NS) transport coefficients for polydisperse granular mixtures of smooth inelastic hard disks or spheres are solved by using the leading terms in a Sonine polynomial expansion. Explicit expressions for all the NS transport coefficients are given in terms of the sizes, masses, compositions, density and restitution coefficients. In addition, the cooling rate is also evaluated to first order in the gradients. The results hold for arbitrary degree of inelasticity and are not limited to specific values of the parameters of the mixture. Finally, a detailed comparison between the derivation of the current theory and previous theories for mixtures is made, with attention paid to the implication of the various treatments employed to date.Comment: 26 pages, to be published in Phys. Rev.

On the Lawrence–Doniach and Anisotropic Ginzburg–Landau Models for Layered Superconductors

The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of both models is given and existence results for their solution are derived. The authors then relate the two models in the sense that they show that as the layer spacing tends to zero, the Lawrence-Doniach model reduces to the anisotropic Ginzburg- Landau model. Finally, simplified versions of the models are derived that can be used to accurately simulate high-temperature superconductors

Mechanistic species distribution modeling reveals a niche shift during invasion

Niche shifts of nonnative plants can occur when they colonize novel climatic conditions. However, the mechanistic basis for niche shifts during invasion is poorly understood and has rarely been captured within species distribution models. We quantified the consequence of between-population variation in phenology for invasion of common ragweed (Ambrosia artemisiifolia L.) across Europe. Ragweed is of serious concern because of its harmful effects as a crop weed and because of its impact on public health as a major aeroallergen. We developed a forward mechanistic species distribution model based on responses of ragweed development rates to temperature and photoperiod. The model was parameterized and validated from the literature and by reanalyzing data from a reciprocal common garden experiment in which native and invasive populations were grown within and beyond the current invaded range. It could therefore accommodate between-population variation in the physiological requirements for flowering, and predict the potentially invaded ranges of individual populations. Northern-origin populations that were established outside the generally accepted climate envelope of the species had lower thermal requirements for bud development, suggesting local adaptation of phenology had occurred during the invasion. The model predicts that this will extend the potentially invaded range northward and increase the average suitability across Europe by 90% in the current climate and 20% in the future climate. Therefore, trait variation observed at the population scale can trigger a climatic niche shift at the biogeographic scale. For ragweed, earlier flowering phenology in established northern populations could allow the species to spread beyond its current invasive range, substantially increasing its risk to agriculture and public health. Mechanistic species distribution models offer the possibility to represent niche shifts by varying the traits and niche responses of individual populations. Ignoring such effects could substantially underestimate the extent and impact of invasions

Modelling the spread and control of Xylella fastidiosa in the early stages of invasion in Apulia, Italy

Xylella fastidiosa is an important plant pathogen that attacks several plants of economic importance. Once restricted to the Americas, the bacterium, which causes olive quick decline syndrome, was discovered near Lecce, Italy in 2013. Since the initial outbreak, it has invaded 23,000 ha of olives in the Apulian Region, southern Italy, and is of great concern throughout Mediterranean basin. Therefore, predicting its spread and estimating the efficacy of control are of utmost importance. As data on this invasive infectious disease are poor, we have developed a spatially-explicit simulation model for X. fastidiosa to provide guidance for predicting spread in the early stages of invasion and inform management strategies. The model qualitatively and quantitatively predicts the patterns of spread. We model control zones currently employed in Apulia, showing that increasing buffer widths decrease infection risk beyond the control zone, but this may not halt the spread completely due to stochastic long-distance jumps caused by vector dispersal. Therefore, management practices should aim to reduce vector long-distance dispersal. We find optimal control scenarios that minimise control effort while reducing X. fastidiosa spread maximally—suggesting that increasing buffer zone widths should be favoured over surveillance efforts as control budgets increase. Our model highlights the importance of non-olive hosts which increase the spread rate of the disease and may lead to an order of magnitude increase in risk. Many aspects of X. fastidiosa disease invasion remain uncertain and hinder forecasting; we recommend future studies investigating quantification of the infection growth rate, and short and long distance dispersal

Inventory and review of quantitative models for spread of plant pests for use in pest risk assessment for the EU territory

This report considers the prospects for increasing the use of quantitative models for plant pest spread and dispersal in EFSA Plant Health risk assessments. The agreed major aims were to provide an overview of current modelling approaches and their strengths and weaknesses for risk assessment, and to develop and test a system for risk assessors to select appropriate models for application. First, we conducted an extensive literature review, based on protocols developed for systematic reviews. The review located 468 models for plant pest spread and dispersal and these were entered into a searchable and secure Electronic Model Inventory database. A cluster analysis on how these models were formulated allowed us to identify eight distinct major modelling strategies that were differentiated by the types of pests they were used for and the ways in which they were parameterised and analysed. These strategies varied in their strengths and weaknesses, meaning that no single approach was the most useful for all elements of risk assessment. Therefore we developed a Decision Support Scheme (DSS) to guide model selection. The DSS identifies the most appropriate strategies by weighing up the goals of risk assessment and constraints imposed by lack of data or expertise. Searching and filtering the Electronic Model Inventory then allows the assessor to locate specific models within those strategies that can be applied. This DSS was tested in seven case studies covering a range of risk assessment scenarios, pest types and dispersal mechanisms. These demonstrate the effectiveness of the DSS for selecting models that can be applied to contribute to EFSA Plant Health risk assessments. Therefore, quantitative spread and dispersal modelling has potential to improve current risk assessment protocols and contribute to reducing the serious impacts of plant pests in Europe

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page