10,265 research outputs found

    Derivation of the Camassa-Holm equations for elastic waves

    Full text link
    In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic medium. We first show that the equation of motion for the nonlocally and nonlinearly elastic medium reduces to the improved Boussinesq equation for a particular choice of the kernel function appearing in the integral-type constitutive relation. We then derive the Camassa-Holm equation from the improved Boussinesq equation using an asymptotic expansion valid as nonlinearity and dispersion parameters tend to zero independently. Our approach follows mainly the standard techniques used widely in the literature to derive the Camassa-Holm equation for shallow water waves. The case where the Fourier transform of the kernel function has fractional powers is also considered and the fractional Camassa-Holm equation is derived using the asymptotic expansion technique.Comment: 15 page

    Whāriki : beyond simple : an exhibition report presented as partial fulfilment of the requirements for the degree of Masters of Māori Visual Arts, Massey University, Palmerston North, New Zealand

    Get PDF
    This thesis/exhibition report is an explication of the significance and relationship of Kai rāranga, rāranga whāriki and their relationship with whānau, hapÅ« and iwi. It explores the impetus behind and relationships important in, and to the production of whāriki. Through the exploration of these relationships the necessity for whāriki wānanga throughout Aotearoa and having wānanga as the preferred medium of imparting knowledge pertaining to rāranga whāriki and for continuity in the production of whāriki is emphasised. It touches on the Māori convention of tono that facilitates interaction between the Kai rārangaresearcher and the Kai tono-researched negating the sometimes invasive convention of ethics approval and formalised contractual obligations. It follows the pathway of author and Kai rāranga, Te Hemo Ata Henareā€™s, coming to be of her mahi whāriki practice. It is an intimate account that extends from function and technique to foundational connectivity to the wider roopu whāriki and those who have preceded us with templates of excellence that recognise the importance of the whakapapa of Māori whakaaro, our epochs and eons of transcendent time and the interconnectedness of all things in and through these patterned processes (Jackson, 2013; Marsden, 2003; Tamanui, 2013). As Karani Sonny Pāpuni said; ā€œā€¦you take this whāriki home with you and then a piece of us will always be with your whānauā€ (Mate ki Tātahi [Sonny] Pāpuni, personal communication, May 17 1991). A clear objective emerging out of this research exercise was to produce a body of work in the form of an exhibition of whāriki and to produce a pictorial and written explication of the process and praxis of whāriki wānanga. However, through the research process, I was returned; i hoki atu ki te timatatanga ō oku mahi, so I could come to know and be. The theme that emerges through rāranga whāriki is the inseparability and the multiplicity of whakapapa and/or whanaungatanga that the Kai rāranga embodies essential for the continuation of the praxis of rāranga whāriki that can only be described as extraordinarily ā€˜Beyond Simpleā€™

    Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies

    Full text link
    We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have one-dimensional approximating Brownian control problems. We propose a simple discrete review policy for controlling such networks. Assuming 2+\epsilon moments on the interarrival times and processing times, we provide a conceptually simple proof of asymptotic optimality of the proposed policy.Comment: Published at http://dx.doi.org/10.1214/105051604000000495 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Multilevel poetry translation as a problem-solving task

    Get PDF
    Poems are treated by translators as hierarchical multilevel systems. Here we propose the notion of ā€œmultilevel poetry translationā€ to characterize such cases of poetry translation in terms of selection and rebuilding of a multilevel system of constraints across languages. Different levels of a poem correspond to different sets of components that asymmetrically constrain each other (e.ā€‰g., grammar, lexicon, syntactic construction, prosody, rhythm, typography, etc.). This perspective allows a poem to be approached as a thinking-tool: an ā€œexperimental labā€ which submits language to unusual conditions and provides a scenario to observe the emergence of new patterns of semiotic behaviour as a result. We describe this operation as a problem-solving task, and exemplify with Augusto de Camposā€™ Portuguese translation of John Donneā€™s poem ā€œThe Expiration.
    • ā€¦
    corecore