4,589 research outputs found
Designing 21st Century Standard Ware: The Cultural Heritage of Leach and the Potential Applications of Digital Technologies
No full textThis practice-based research investigates the potential applications of digital manufacturing technologies in the design and production of hand-made tableware at the Leach Pottery. The methodology for the research establishes an approach grounded in my previous experience as a maker that is informed by an open, experimental, emergent, and responsive framework based on Naturalistic Inquiry.
A critical contextual review describes the cultural heritage of Leach which, for the purposes of the research, is developed through the Leach Pottery as a significant site, the historical production of the iconic Leach Standard Ware and the contemporary production of Leach Tableware. This is followed by an examination of Potter’s Tools in the Leach production environment, and a review of makers’ digital ceramic practice.
The contextual review is followed by an explication of ‘standards’ presented through visual lineages of Standard Ware and Leach Tableware to define ‘standard’ at a design (macro) level, followed by an examination of how ‘standard’ operates at a making (micro level) level. This chapter presents new knowledge in relation to defining the visual field of Leach Pottery tableware production and its standards of design.
A chapter focussed on practice presents the outcomes and analysis of my engagement with digital manufacturing technologies which resulted in the development of new tools to support Leach Tableware production and the interrogation of Leach forms, in different mediums, which led to the creation of Digital-Analogue Leach forms. The practice culminated in the design and development of new 21st century Standard Ware: a range of 9 forms, called Echo of Leach, that were developed by myself using digital and analogue methods: the designs were realised by myself, the Leach Studio, and a further four makers. The outcomes of the research were presented in a three month exhibition at the Leach Pottery in 2013.
The conclusions of the research draw on the key points raised in the analysis of the practice and relate these to the approaches to making pottery that are highlighted in the cultural heritage of Leach in the contextual review. These are also discussed in relation to ways in which these findings could be taken forward into development of knowledge about Standard Ware, especially in a broader studio pottery context
Jacobi's last multiplier and the complete symmetry group of the Ermakov-Pinney equation
No full textThe Ermakov-Pinney equation possesses three Lie point symmetries with the algebra sl(2, R). This algebra does not provide a representation of the complete symmetry group of the Ermakov-Pinney equation. We show how the representation of the group can be obtained with the use of the method described in Nucci, J. Nonlin. Math. Phys. 12 ( 2005) ( this issue), which is based on the properties of Jacobi's last multiplier (Bianchi L, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni, Enrico Spoerri, Pisa, 1918), the method of reduction of order ( Nucci, J. Math. Phys 37 ( 1996), 1772 - 1775) and an interactive code for calculating symmetries ( Nucci, Interactive REDUCE programs for calcuating classical, non-classical and Lie-Backlund symmetries for differential equations (preprint: Georgia Institute of Technology, Math 062090-051, 1990, and CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 3: New Trends in Theoretical Developments and Computational Methods, Editor: Ibragimov N H, CRC Press, Boca Raton, 1996, 415 - 481)
The Jacobi Last Multiplier and its Applications in Mechanics
No full textWe exploit the relationships between the Lie symmetries of a mechanical system, the Jacobi Last Multiplier and the Lagrangian of the system to construct alternative Lagrangians and first integrals in the case that there is a generous supply of symmetry. A Liénard-type nonlinear oscillator is used as an example. We also exemplify the sometimes impossible connection between the general solution of a dynamical system and its first integrals
The method of Ostrogradsky, quantization, and a move toward a ghost-free future
No full textThe method of Ostrogradsky has been used to construct a first-order Lagrangian, hence Hamiltonian, for the fourth-order field-theoretical model of Pais–Uhlenbeck with unfortunate results when quantization is undertaken since states with negative norm, commonly called “ghosts,” appear. We propose an alternative route based on the preservation of symmetry and this leads to a ghost-free quantization
Point and counterpoint between Mathematical Physics and Physical Mathematics
No full textIn recent years there has been a resurgence of interest in problems dating back for over half a century. In particular we refer to the questions of the consistency of quantisation and nonlinear canonical transformations and the quantisation of higher-order field theories. We present resolutions to these questions based upon considerations of symmetry. This enables one to examine these problems within the context of existing theory without the need to introduce new and exotic theories
Gauge variant symmetries for the Schrodinger equation
No full textThe last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the Schrödinger equation for a one-degree-of-freedom system with a constant multiplier. In the sequel we consider the particular example of the simple harmonic oscillator. In the case of the general equation for the simple harmonic oscillator which contains an arbitrary function we show that all Schrödinger equations possess the same number of Lie point symmetries with the same algebra. Prom the symmetries we construct the solutions of the Schrödinger equation and find that they differ only by a phase determined by the gauge
Lie integrable cases of the simplified multistrain/two-stream model for tuberculosis and Dengue fever
No full textWe apply the techniques of Lie’s symmetry analysis to a caricature of the simplified multistrain model
of Castillo-Chavez and Feng [C. Castillo-Chavez, Z. Feng, To treat or not to treat: The case of tuberculosis,
J. Math. Biol. 35 (1997) 629–656] for the transmission of tuberculosis and the coupled two-stream vectorbased
model of Feng and Velasco-Hernández [Z. Feng, J.X. Velasco-Hernández, Competitive exclusion in
a vector-host model for the dengue fever, J. Math. Biol. 35 (1997) 523–544] to identify the combinations of
parameters which lead to the existence of nontrivial symmetries. In particular we identify those combinations
which lead to the possibility of the linearization of the system and provide the corresponding solutions.
Many instances of additional symmetry are analyzed
An old method of Jacobi to find Lagrangians
No full textIn a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi's method
Singularity Analysis and Integrability of a Simplified Multistrain Model for the Transmission of Tuberculosis and Dengue Fever
No full textWe apply singularity analysis to a caricature of the simplified multistrain model of Castillo-Chavez and Feng (J Math Biol 35 (1997) 629-656) for the transmission of tuberculosis and the coupled two-stream vector-based model of Feng and Velasco-Hernandez (J Math Biol 35 (1997) 523-544) to identify values of the parameters for which the system of nonlinear first-order ordinary differential equations describing the model are integrable. A number of combinations of parameters for which the system is integrable are identified. We compare them with the results we obtained by a symmetry analysis in an earlier paper (J Math Anal Appl 333 (2007) 430-449
Some Lagrangians for Systems without a Lagrangian
No full textWe demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle
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