An eigenproblem approach to classical screw theory

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general two-, three-systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. We also present novel methods for the determination of the principal screws for four-, five-systems which do not require the explicit computation of the reciprocal systems. Principal screws of the systems of different orders are identified from one uniform criterion, namely that the pitches of the principal screws are the extreme values of the pitch.The classical results of screw theory, namely the equations for the cylindroid and the pitch-hyperboloid associated with the two-and three-systems, respectively have been derived within the proposed framework. Algebraic conditions have been derived for some of the special screw systems. The formulation is also illustrated with several examples including two spatial manipulators of serial and parallel architecture, respectively.

The non-literary Latin letters. A study of their syntax and pragmatics

This dissertation studies the language of Latin letters that were written in Egypt and Vindolanda (in northern Britain) during the period 1st century BC 3rd century AD on papyri, ostraca, and wooden tablets. The majority of the texts is, in one way or another, connected with the Roman army. The focus of the study is on syntax and pragmatics. Besides traditional philological methods, modern syntactic theory is used as well, especially in the pragmatic analysis. The study begins with a critical survey of certain concepts that are current in the research on the Latin language, most importantly the concept of vulgar Latin , which, it is argued, seems to be used as an abstract noun for variation and change in Latin . Further, it is necessary to treat even the non-literary material primarily as written texts and not as straightforward reflections of spoken language. An examination of letter phraseology shows that there is considerable variation between the two major geographical areas of provenance. Latin letter writing in Egypt was influenced by Greek. The study highlights the importance of seeing the letters as a text type, with recurring phraseological elements appearing in the body text as well. It is argued that recognising these elements is essential for the correct analysis of the syntax. Three areas of syntax are discussed in detail: sentence connection (mainly parataxis), syntactically incoherent structures and word order (the order of the object and the verb). For certain types of sentence connection we may plausibly posit an origin in spoken Latin, but for many other linguistic phenomena attested in this material the issue of spoken Latin is anything but simple. Concerning the study of historical syntax, the letters offer information about the changing status of the accusative case. Incoherent structures may reflect contaminations in spoken language but usually the reason for them is the inability of the writer to put his thoughts into writing, especially when there is something more complicated to be expressed. Many incoherent expressions reflect the need to start the predication with a thematic constituent. Latin word order is seen as resulting from an interaction of syntactic and pragmatic factors. The preference for an order where the topic is placed sentence-initially can be seen in word order more generally as well. Furthermore, there appears a difference between Egypt and Vindolanda. The letters from Vindolanda show the order O(bject) V(erb) clearly more often than the letters from Egypt. Interestingly, this difference correlates with another, namely the use of the anaphoric pronoun is. This is an interesting observation in view of the fact that both of these are traditional Latin features, as opposed to those that foreshadow the Romance development (VO order and use of the anaphoric ille). However, it is difficult to say whether this is an indication of social or regional variation.

Ancient Philosophers on Mental Illness

This dissertation is about ancient philosophers notions of mental illness, from Plato onwards. Mental illness here means disorders that, in ancient medical thought, were believed to originate in the body but to manifest themselves predominantly through mental symptoms. These illnesses were treated by physical means, which were believed to address the bodily cause of the illness, conceived of as an elemental imbalance or a state of cephalic stricture , for example. Sometimes the mental symptoms were addressed directly by psychotherapeutic means. The first and most important question explored concerns how the ancient philosophers responded to the medical notion of mental illness, and how they explained such illnesses in their theories of physiology and psychology. Although the illnesses are seldom discussed extensively, the philosophers were well aware of their existence and regarded their occurrence an indication of the soul s close dependence on the body. This called for a philosophical account. The second question addressed has to do with the ancient philosophers role as experts in mental problems of a non-medical kind, such as unwanted emotions. These problems were dubbed diseases of the soul , and the philosophers thus claimed to be doctors of the soul. Although the distinction between mental illnesses and diseases of the soul was often presented as rather obvious, there was some vagueness and overlap. There is still a third question that is explored, concerning the status of both mental illnesses and diseases of the soul as unnatural conditions, the role of the human body in the philosophical aetiologies of evil, and the medico-philosophical theories of psycho-physiological temperaments. This work consists of an introduction and five main chapters, focusing on Plato, Aristotle, the Stoics and Galen, and the Sceptics, the Epicureans and later Platonists. The sources drawn on are the original Greek and Latin philosophical and medical texts. It appears that the philosophers accepted the medical notion of mental illness, but interpreted it in various ways. The differences in interpretation were mostly attributable to differences in their theories of the soul. Although the distinction between mental illness and diseases of the soul was important, marking the boundary between the fields of expertise of medicine and philosophy, and of the individual s moral responsibilities, the problematic aspects of establishing it are discussed rather little in ancient philosophy. There may have been various reasons for this. The medical descriptions of mental illness are often extreme, symptoms of the psychotic type excluding the possibility of the condition being of the non-medical kind. In addition, the rigid normativeness of ancient philosophical anthropologies and their rigorous notion of human happiness decreased the need to assess the acceptability of individual variation in their emotional and intellectual lives and external behaviour.

Patterns of Transcendence : Classical Myth in Marina Tsvetaeva's Poetry of the 1920s

This study examines the position and meaning of Classical mythological plots, themes and characters in the oeuvre of the Russian Modernist poet Marina Tsvetaeva (1892-1941). The material consists of lyric poems from the collection Posle Rossii (1928) and two longer lyrical tragedies, Ariadna (1924) and Fedra (1927). These works are examined in the context of Russian Modernism and Tsvetaeva s own poetic development, also taking into account the author s biography, namely, her correspondence with Boris Pasternak. Tsvetaeva s appropriations of the myths enter into a dialogue with the Classical tradition and with the earlier Russian and Western literary manifestations of the source material. Her Classical texts are inextricably linked with her own authorial myth, they are used to project both her ideas about poetry as well as the authored self of her poems. An important context for Tsvetaeva s application of the Classical myths is the concept of the Platonic ladder of Eros. This plot evokes the process of transcendence of the mortal subject into the immaterial realm and is applied by the author as an extended metaphor of the poet s birth. Emphasizing the dialectical movement between the earthly and the divine, Tsvetaeva s Classical personae foreground various positions of the individual between these two realms. By means of kaleidoscopic reformulations of similar metaphors and concepts, Tsvetaeva s mythological poems illustrate the poet s position between the material and the immaterial and the various consequences of this dichotomy on the creative mission. At the heart of Tsvetaeva s appropriation of the Sibyl, Phaedra, Eurydice and Ariadne is the tension between the body and disembodiment. The two lyrical tragedies develop the dichotomous worldview further, nevertheless emphasizing the dual perspective of the divine and the earthly realms: immaterial existence is often evaluated from a material perspective and vice versa. The Platonic subtext is central for Ariadna, focussing on Theseus development from an earthly hero to a spiritual one. Fedra concentrates on Phaedra s divinely induced physical passion, which is nevertheless evoked in a creative light.

Transient state work fluctuation theorem for a classical harmonic oscillator linearly coupled to a harmonic bath

Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.

Classical and Cosserat plasticity and viscoplasticity models for slow granular flow

We consider models for the rheology of dense, slowly deforming granular materials based of classical and Cosserat plasticity, and their viscoplastic extensions that account for small but finite particle inertia. We determine the scale for the viscosity by expanding the stress in a dimensionless parameter that is a measure of the particle inertia. We write the constitutive relations for classical and Cosserat plasticity in stress-explicit form. The viscoplastic extensions are made by adding a rate-dependent viscous stress to the plasticity stress. We apply the models to plane Couette flow, and show that the classical plasticity and viscoplasticity models have features that depart from experimental observations; the prediction of the Cosserat viscoplasticity model is qualitatively similar to that of Cosserat plasticity, but the viscosities modulate the thickness of the shear layer.

NMR relaxation study of disorder in the mixed system BP x GPI(1-x) and the low temperature transition from classical to quantum rotation

1H NMR spin-lattice relaxation time (T1) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BPxGPI(1-x)), to study the effects of disorder on the proton group dynamics. Analysis of T1 data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (Ea) and the torsional energy gap (E01). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

Evaluation of Ustilago sporoboli-indici as a classical biological control agent for invasive Sporobolus grasses in Australia

Sporobolus pyramidalis, S. africanus, S. natalensis, S. fertilis and S. jacquemontii, known collectively as the weedy Sporobolus grasses, are exotic weeds causing serious economic losses in grazing areas along Australia's entire eastern coast. In one of the first attempts to provide biological control for a grass, the potential of a smut, Ustilago sporoboli-indici, as a biological control agent for all five weedy Sporobolus spp. found in Australia was evaluated in glasshouse studies. Application of basidiospores to 21-day-old Sporobolus seedlings and subsequent incubation in a moist chamber (26 °C, 90% RH, 48 h) resulted in infection of S. pyramidalis, S. africanus, S. natalensis and S. fertilis but not S. jacquemontii. Host-range trials with 13 native Australian Sporobolus spp. resulted in infection of four native species. Evaluation of damage caused by the smut on two Australian native and two weedy Sporobolus spp. showed that the total numbers of flowers infected for the four grasses were in the following order: S. creber > S. fertilis > S. elongatus > S. natalensis with percentage flower infections of 21%, 14%, 12% and 3%, respectively. Significant differences (P = 0.001) were found when the numbers of infected flowers caused by each treatment were compared. The infection of the four native Sporobolus spp. by the smut indicated that it was not sufficiently host specific for release in Australia and the organism was rejected as a potential biological control agent. The implications of these results are discussed.

Studies on the rust Prospodium tuberculatum, a new classical biological control agent released against the invasive alien weed Lantana camara in Australia. 2. Host range

A strain of the rust Prospodium tuberculatum from Brazil was screened as a potential biocontrol agent against 40 Australian Lantana camara forms and 52 closely related, non-target plant species. Results under glasshouse conditions showed that the Brazilian rust strain is pathogenic to only two flower colour forms: pink and pink-edged red. Macro- and microsymptoms were recorded using 11 assessment categories and four susceptibility ratings. No macrosymptoms were observed on any of the non-target plants.

A review of Australian classical biological control of weeds programs and research activities over the past 12 years

Considerable progress has been made towards the successful classical biological control of many of Australia’s exotic weeds over the past decade. Some 43 new arthropod or pathogen agents were released in 19 projects. Effective biological control was achieved in several projects with the outstanding successes being the control of rubber vine, Cryptostegia grandiflora, and bridal creeper, Asparagus asparagoides. Significant developments also occurred in target prioritization, procedures for target and agent approval, funding, infrastructure and cooperation between agencies. Scientific developments included greater emphasis on climate matching, plant and agent phylogeny, molecular diagnostics, agent prioritization and agent evaluation.

Classical Biological Control for the Protection of Natural Ecosystems.

Of the 70 cases of classical biological control for the protection of nature found in our review, there were fewer projects against insect targets (21) than against invasive plants (49), in part, because many insect biological control projects were carried out against agricultural pests, while nearly all projects against plants targeted invasive plants in natural ecosystems. Of 21 insect projects, 81% (17) provided benefits to protection of biodiversity, while 48% (10) protected products harvested from natural systems, and 5% (1) preserved ecosystem services, with many projects contributing to more than one goal. In contrast, of the 49 projects against invasive plants, 98% (48) provided benefits to protection of biodiversity, while 47% (23) protected products, and 25% (12) preserved ecosystem services, again with many projects contributing to several goals. We classified projects into complete control (pest generally no longer important), partial control (control in some areas but not others), and "in progress," for projects in development for which outcomes do not yet exist. For insects, of the 21 projects discussed, 59% (13) achieved complete control of the target pest, 18% (4) provided partial control, and 41% (9) are still in progress. By comparison, of the 49 invasive plant projects considered, 27% (13) achieved complete control, while 33% (16) provided partial control, and 47% (24) are still in progress. For both categories of pests, some projects' success ratings were scored twice when results varied by region. We found approximately twice as many projects directed against invasive plants than insects and that protection of biodiversity was the most frequent benefit of both insect and plant projects. Ecosystem service protection was provided in the fewest cases by either insect or plant biological control agents, but was more likely to be provided by projects directed against invasive plants, likely because of the strong effects plants exert on landscapes. Rates of complete success appeared to be higher for insect than plant targets (59% vs 27%), perhaps because most often herbivores gradually weaken, rather than outright kill, their hosts, which is not the case for natural enemies directed against pest insects. For both insect and plant biological control, nearly half of all projects reviewed were listed as currently in progress, suggesting that the use of biological control for the protection of wildlands is currently very active.