On quasi-degeneracies in plate vibration problems

In plotting the variation of frequencies with geometric parameters such as side ratio, skew angle, thickness taper, etc. in detailed studies of the vibration characteristics of plates, situations are encountered such as crossing of the frequency curves or the tendency of these curves to come close together and veer away from each other. These have been generally referred to as “frequency crossings” and “transitions” respectively. The latter may preferably be referred to as “quasi-degeneracies”. In the literature there appears to be some ambiguity in the analysis and interpretation of these features. In this paper, a clarification of some of these questions as regards rectangular and skew plates is presented by making use of concepts from physics dealing with molecular vibrations.

Whole-genome sequencing reveals untapped genetic potential in Africa’s indigenous cereal crop sorghum

Sorghum is a food and feed cereal crop adapted to heat and drought and a staple for 500 million of the world’s poorest people. Its small diploid genome and phenotypic diversity make it an ideal C4 grass model as a complement to C3 rice. Here we present high coverage (16-45 × ) resequenced genomes of 44 sorghum lines representing the primary gene pool and spanning dimensions of geographic origin, end-use and taxonomic group. We also report the first resequenced genome of S. propinquum, identifying 8 M high-quality SNPs, 1.9 M indels and specific gene loss and gain events in S. bicolor. We observe strong racial structure and a complex domestication history involving at least two distinct domestication events. These assembled genomes enable the leveraging of existing cereal functional genomics data against the novel diversity available in sorghum, providing an unmatched resource for the genetic improvement of sorghum and other grass species.

Screening and breeding for genetic resistance to anthracnose in mango

Postharvest diseases remain a significant constraint to the transport, storage and marketing of mangoes. The two main ones are anthracnose and stem end rot. Anthracnose caused by Colletotrichum gloeosporioides is the more wide-spread of the two. Varieties within Mangifera indica are known to vary in their level of reactions to anthracnose; however, the best tolerance in current commercial cultivars is not sufficient to eliminate the need for pre- and postharvest fungicides treatments. A screening program was initiated in mango accessions in the Australian National Mango Genebank to look for any significant resistance to C. gloeosporioides in fruit as they ripened. Screening was conducted by rating reactions to natural infection of anthracnose and reactions to artificially inoculating fruit with virulent isolates of C. gloeosporioides. A range of reactions to the pathogen were identified, with strong resistance found in one accession of the species M. laurina. This accession was used as the pollen parent in a controlled crossing program with a M. indica hybrid from the Australian Mango Breeding Program (AMBP). Sixty successful hybrids between the species have been generated. The hybrid population will be screened for resistance to anthracnose and used for gene discovery investigations to identify markers for anthracnose resistance.

Early-season movement dynamics of phytophagous pest and natural enemies across a native vegetation-crop ecotone

There is limited understanding about how insect movement patterns are influenced by landscape features, and how landscapes can be managed to suppress pest phytophage populations in crops. Theory suggests that the relative timing of pest and natural enemy arrival in crops may influence pest suppression. However, there is a lack of data to substantiate this claim. We investigate the movement patterns of insects from native vegetation (NV) and discuss the implications of these patterns for pest control services. Using bi-directional interception traps we quantified the number of insects crossing an NV/crop ecotone relative to a control crop/crop interface in two agricultural regions early in the growing season. We used these data to infer patterns of movement and net flux. At the community-level, insect movement patterns were influenced by ecotone in two out of three years by region combinations. At the functional-group level, pests and parasitoids showed similar movement patterns from NV very soon after crop emergence. However, movement across the control interface increased towards the end of the early-season sampling period. Predators consistently moved more often from NV into crops than vice versa, even after crop emergence. Not all species showed a significant response to ecotone, however when a response was detected, these species showed similar patterns between the two regions. Our results highlight the importance of NV for the recruitment of natural enemies for early season crop immigration that may be potentially important for pest suppression. However, NV was also associated with crop immigration by some pest species. Hence, NV offers both opportunities and risks for pest management. The development of targeted NV management may reduce the risk of crop immigration by pests, but not of natural enemies.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Gene flow from Corymbia hybrids in northern New South Wales

Some of the most productive taxa for forestry are interspecific F1 hybrids grown as exotics in the tropics and subtropics. Attributes of resilience, adaptability and vigour which engender the hybrids for wood production, may also exacerbate the risk they present from gene flow to native species gene pools or to local ecologies as weeds. To determine the biological and genetic factors that influence the extent of hybridisation, we examine the distribution and genealogy of wildlings surrounding plantings of locally-exotic Corymbia torelliana (Section Cadageria) near native C. henryi (Section Maculatae) in northern New South Wales. Our study showed pre-mating and pre- and post-zygotic barriers were incomplete, with in situ generation and natural establishment of both F1 hybrids (n = 3) and advanced generation hybrids under the disturbed conditions bordering native forest. As hybrids were located on alluvial flats exposed to frost, they also likely have an extended ecological range relative to native C. henryi. Despite the likely generation of large viable seed crops on F1 trees at the site over many years, establishment success and survival of advanced generation hybrids may be low, as only 5 immature and no mature advanced generation hybrids were identified. Propagation and genetic analysis of a seed crop from one F1 wildling showed early survival and vigour of seedlings in cultivation was high, and that at least for some F1 in some seasons, backcrossing to the recurrent native C. henryi parent is favoured (60%), whereas selfing (10%) and crossing with other F1 (30%) was less frequent. Transport of seed by stingless bees probably accounted for long distance dispersal from C. torelliana, but this mechanism does not appear to supplement gravity-dispersal of seed from the F1. Coupled with other evidence from studies of bee behaviour, controlled pollination in Corymbia sp., and long-term fitness in second generation eucalypt hybrids, we anticipate gene flow via pollen rather than seed will be the greater challenge for managing the risk of introgression of C. torelliana ancestry into native species from the planted F1 hybrid. If large sources of F1 pollen become available to compete with native pollen, gene flow will probably be frequent and hybrids may establish in disturbed conditions and in habitats beyond the ecological range of their native parent. Further study is needed to determine the degree to which outbreeding depression and poor survival inhibits on-going gene flow.

Rwanda Crisis and Genocide in Case Law of Rwanda Tribunal

After the Second World War the public was shocked to learn about the horrors perpetrated. As a response to the Holocaust, the newly established United Nations adopted the Genocide Convention of 1948 to prevent future genocides and to punish the perpetrators. The Convention remained, however, almost dead letter until the present day. In 1994, the long-lasted tension between the major groups of Hutu and Tutsi in Rwanda erupted in mass scale violence towards the Tutsi ethnic group. The purpose was to eradicate the Tutsi population of Rwanda. The international community did not halt the genocide. It stood by idle, failing to follow the swearing-in of the past. The United Nations established the International Criminal Tribunal for Rwanda (the ICTR) to bring to justice persons responsible for the genocide. Ever since its creation the ICTR has delivered a wealth of judgements elucidating the legal ingredients of the crime of genocide. The case law on determining the membership of national, ethnic, racial or religious groups has gradually shifted from the objective to subjective position. The membership of a group is seen as a subjective rather than objective concept. However, a totally subjective approach is not accepted. Therefore, it is necessary to determine some objective existence of a group. The provision on the underlying offences is not so difficult to interpret compared to the corresponding one on the protected groups and the mental element of genocide. The case law examined, e.g., whether there is any difference between the words killing and meurtre, the nature of mental harm caused by the perpetrator and sexual violence in the conflict. The mental element of genocide or dolus specialis of genocide is not thoroughly examined in the case law of the ICTR. In this regard, reference in made, in addition, to the case law of the other ad hoc Tribunal. The ICTR has made a significant contribution to the law of genocide and international criminal justice in general. The corpus of procedural and substantive law constitutes a basis for subsequent trials in international and hybrid tribunals. For national jurisdictions the jurisprudence on substantive law is useful while prosecuting international crimes.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

The church must become the people of Soweto : Manas Buthelezi’s existential-Christocentric understanding of the church

The aim of this study has been to discern what Manas Buthelezi (1935-), a black South African Lutheran theologian and later also a bishop, regards as the requirements a church has to fulfill in order to be credible in the apartheid society. Buthelezi’s dissertation and several articles written between the years 1968 and 1993 are the sources of this study. Also the lectures held in Heidelberg in 1972 are referred to. Systematic analysis is the method used. The question of the credibility of the church is studied through three concepts that play an important role in Buthelezi’s ecclesiological thought, namely the wholeness of life, incarnation and liberation. The notion of the wholeness of life stems from the African tradition. Buthelezi takes the concept into the Christian church: the church should realize that God is the Creator of all life and Christ the lord of every aspect of human existence. Life is one entity coram Deo. However, the church is not to become the world; solidarity between the two must remain critical as the church is also called to play a prophetic role in the society. The church is in an open relationship with the world. It has a unique message of forgiveness and reconciliation. Nevertheless, the message is not a possession of the church but it is addressed to the whole world. The meaning of incarnation comes close to that of the wholeness of life. Following the example of Christ’s incarnation, the church must become human in the reality of the people. The church in Soweto is to become the people of Soweto, that is, the church must become as vulnerable as the people are. An incarnate church cannot be immune to the oppression that people experience, because the people are the church. The church is therefore bound to suffer. Buthelezi’s theology of the cross is pragmatic: the suffering of the church aims at the liberation of the oppressed. At times the physical presence of the church by the side of the suffering people is the only way to preach the incarnate gospel. In the South Africa of the late 1960s onwards the liberation of the oppressed black people was high on the agenda of Black Theology. As a leader of the early South African Black Theology, Buthelezi is concerned about the racial injustice in his country. He urges the churches to join the struggle against it as one people of God. The notions of liberation and the wholeness of life emerge in Buthelezi’s holistic understanding of liberation that involves the inner liberation of the black spirit and the liberation of the economic, social and political aspects of life. Interpreting Tillich’s correlation method in the South African situation, and also paralleling other liberation theologians, Buthelezi takes the existential situation of the people as the starting point for liberation. The gospel has to respond to the existential questions of people. The church is called to work for the liberation of society but it must also be liberated itself. Buthelezi initiated the LWF statement on the status confessionis in South Africa (1977). In line with the statement, he calls for church unity on the human level. For the unity to be true, it has to be experienced on the grassroots’ level. All the three concepts covered urge the church to come down from any ivory tower and out of any spiritual haven it might hide in. A lot of the credibility of the church derives from the behavior of the people. Buthelezi’s concentration on how the people who constitute the church should live their faith leaves less attention to how God constitutes the church. I have labeled Buthelezi’s understanding of the church existential-Christocentric due to the emphasis he lays on the need of the church to take the existential situation of the people seriously and on the other hand, on Christ as the exemplar for the church.

The Electronic Structure of Graphite from Compton Profile Measurements

Compton profile data are used to investigate the ground state wavefunction of graphite. The results of two new $\gamma$-ray measurements are reported and compared with the results of earlier $\gamma$-ray and electron scattering measurements. A tight-binding calculation has been carried out and the results of earlier calculations based on a molecular model and a pseudo-potential wavefunction are considered. The analysis, in terms of the reciprocal form factor, shows that none of the calculations gives an adequate description of the data in the basal plane although the pseudo-potential calculation describes the anisotropy in the plane reasonably well. In the basal plane the zero-crossing theorem appears to be violated and this problem must be resolved before more accurate models can be derived. In the c-axis direction the molecular model and the tight binding calculation give better agreement with the experimental data than does the pseudopotential calculation.

Should tax incentives for charitable giving stop at Australia's borders?

Around the world, philanthropic gifts are increasingly crossing borders, driven by globalisation and facilitated by liberalised cross-border tax incentives. Australia is considered to have one of the strictest regimes for the tax treatment of cross-border donations. With bipartisan political support for a significant reduction in the amount and scope of Australian foreign aid, the nation’s international presence through the ‘soft power’ of aid will fall increasingly upon private philanthropy. Are the current tax incentives for Australian cross-border philanthropy and the supervision of those incentives appropriate to both facilitate and regulate international giving? To address this question, this article analyses the amount of Australian cross-border philanthropy and explains the current legislative architecture affecting the tax deductibility of cross-border gifts. It then examines the Australian Government’s proposed ‘in Australia’ reform agenda against the underlying fiscal and regulatory policy imperatives, and makes recommendations for the future tax treatment of Australian cross-border philanthropy.

The perturbational treatment of the process of hydrogen abstraction by ketones

The change in energy during hydrogen abstraction by ketones is estimated for different electronic states as a function of the intermolecular orbital overlap employing perturbation theory. The results suggest that ketones preferentially undergo the in-plane reaction and abstract a hydrogen atom in their triplet nπ* state. For ketones where the triplet ππ* state lies below the triplet nπ* state, hydrogen abstraction can take place in the ππ* state owing to the crossing of the zero order reaction surfaces of the nπ* and ππ* states.

Experiments on the fine structure of turbulence

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings. It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings. The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.

Entry of the membrane-containing bacteriophages into their hosts

Viruses are biological entities able to replicate only within their host cells. Accordingly, entry into the host is a crucial step of the virus life-cycle. The focus of this study was the entry of bacterial membrane-containing viruses into their host cells. In order to reach the site of replication, the cytoplasm of the host, bacterial viruses have to traverse the host cell envelope, which consists of several distinct layers. Lipid membrane is a common feature among animal viruses but not so frequently observed in bacteriophages. There are three families of icosahedral bacteriophages that contain lipid membranes. These viruses belong to families Cystoviridae, Tectiviridae, and Corticoviridae. During the course of this study the entry mechanisms of phages representing the three viral families were investigated. We employed a range of microbiological, biochemical, molecular biology and microscopy techniques that allowed us to dissect phage entry into discrete steps: receptor binding, penetration through the outer membrane, crossing the peptidoglycan layer and interaction with the cytoplasmic membrane. We determined that bacteriophages belonging to the Cystoviridae, Tectiviridae, and Corticoviridae viral families use completely different strategies to penetrate into their host cells.