Propriétés géométriques des surfaces associées aux solutions des modèles sigma grassmanniens en deux dimensions

Dans cette thèse, nous analysons les propriétés géométriques des surfaces obtenues des solutions classiques des modèles sigma bosoniques et supersymétriques en deux dimensions ayant pour espace cible des variétés grassmanniennes G(m,n). Plus particulièrement, nous considérons la métrique, les formes fondamentales et la courbure gaussienne induites par ces surfaces naturellement plongées dans l'algèbre de Lie su(n). Le premier chapitre présente des outils préliminaires pour comprendre les éléments des chapitres suivants. Nous y présentons les théories de jauge non-abéliennes et les modèles sigma grassmanniens bosoniques ainsi que supersymétriques. Nous nous intéressons aussi à la construction de surfaces dans l'algèbre de Lie su(n) à partir des solutions des modèles sigma bosoniques. Les trois prochains chapitres, formant cette thèse, présentent les contraintes devant être imposées sur les solutions de ces modèles afin d'obtenir des surfaces à courbure gaussienne constante. Ces contraintes permettent d'obtenir une classification des solutions en fonction des valeurs possibles de la courbure. Les chapitres 2 et 3 de cette thèse présentent une analyse de ces surfaces et de leurs solutions classiques pour les modèles sigma grassmanniens bosoniques. Le quatrième consiste en une analyse analogue pour une extension supersymétrique N=2 des modèles sigma bosoniques G(1,n)=CP^(n-1) incluant quelques résultats sur les modèles grassmanniens. Dans le deuxième chapitre, nous étudions les propriétés géométriques des surfaces associées aux solutions holomorphes des modèles sigma grassmanniens bosoniques. Nous donnons une classification complète de ces solutions à courbure gaussienne constante pour les modèles G(2,n) pour n=3,4,5. De plus, nous établissons deux conjectures sur les valeurs constantes possibles de la courbure gaussienne pour G(m,n). Nous donnons aussi des éléments de preuve de ces conjectures en nous appuyant sur les immersions et les coordonnées de Plücker ainsi que la séquence de Veronese. Ces résultats sont publiés dans la revue Journal of Geometry and Physics. Le troisième chapitre présente une analyse des surfaces à courbure gaussienne constante associées aux solutions non-holomorphes des modèles sigma grassmanniens bosoniques. Ce travail généralise les résultats du premier article et donne un algorithme systématique pour l'obtention de telles surfaces issues des solutions connues des modèles. Ces résultats sont publiés dans la revue Journal of Geometry and Physics. Dans le dernier chapitre, nous considérons une extension supersymétrique N=2 du modèle sigma bosonique ayant pour espace cible G(1,n)=CP^(n-1). Ce chapitre décrit la géométrie des surfaces obtenues des solutions du modèle et démontre, dans le cas holomorphe, qu'elles ont une courbure gaussienne constante si et seulement si la solution holomorphe consiste en une généralisation de la séquence de Veronese. De plus, en utilisant une version invariante de jauge du modèle en termes de projecteurs orthogonaux, nous obtenons des solutions non-holomorphes et étudions la géométrie des surfaces associées à ces nouvelles solutions. Ces résultats sont soumis dans la revue Communications in Mathematical Physics.

Acoustic radiation and scattering from cylindrical bodies and analysis of transducer arrays

New mathematical methods to analytically investigate linear acoustic radiation and scattering from cylindrical bodies and transducer arrays are presented. Three problems of interest involving cylinders in an infinite fluid are studied. In all the three problems, the Helmholtz equation is used to model propagation through the fluid and the beam patterns of arrays of transducers are studied. In the first problem, a method is presented to determine the omni-directional and directional far-field pressures radiated by a cylindrical transducer array in an infinite rigid cylindrical baffle. The solution to the Helmholtz equation and the displacement continuity condition at the interface between the array and the surrounding water are used to determine the pressure. The displacement of the surface of each transducer is in the direction of the normal to the array and is assumed to be uniform. Expressions are derived for the pressure radiated by a sector of the array vibrating in-phase, the entire array vibrating in-phase, and a sector of the array phase-shaded to simulate radiation from a rectangular piston. It is shown that the uniform displacement required for generating a source level of 220 dB ref. μPa @ 1m that is omni directional in the azimuthal plane is in the order of 1 micron for typical arrays. Numerical results are presented to show that there is only a small difference between the on-axis pressures radiated by phased cylindrical arrays and planar arrays. The problem is of interest because cylindrical arrays of projectors are often used to search for underwater objects. In the second problem, the errors, when using data-independent, classical, energy and split beam correlation methods, in finding the direction of arrival (DOA) of a plane acoustic wave, caused by the presence of a solid circular elastic cylindrical stiffener near a linear array of hydrophones, are investigated. Scattering from the effectively infinite cylinder is modeled using the exact axisymmetric equations of motion and the total pressures at the hydrophone locations are computed. The effect of the radius of the cylinder, a, the distance between the cylinder and the array, b, the number of hydrophones in the array, 2H, and the angle of incidence of the wave, α, on the error in finding the DOA are illustrated using numerical results. For an array that is about 30 times the wavelength and for small angles of incidence (α<10), the error in finding the DOA using the energy method is less than that using the split beam correlation method with beam steered to α; and in some cases, the error increases when b increases; and the errors in finding the DOA using the energy method and the split beam correlation method with beam steered to α vary approximately as a7 / 4 . The problem is of interest because elastic stiffeners – in nearly acoustically transparent sonar domes that are used to protect arrays of transducers – scatter waves that are incident on it and cause an error in the estimated direction of arrival of the wave. In the third problem, a high-frequency ray-acoustics method is presented and used to determine the interior pressure field when a plane wave is normally incident on a fluid cylinder embedded in another infinite fluid. The pressure field is determined by using geometrical and physical acoustics. The interior pressure is expressed as the sum of the pressures due to all rays that pass through a point. Numerical results are presented for ka = 20 to 100 where k is the acoustic wavenumber of the exterior fluid and a is the radius of the cylinder. The results are in good agreement with those obtained using field theory. The directional responses, to the plane wave, of sectors of a circular array of uniformly distributed hydrophones in the embedded cylinder are then computed. The sectors are used to simulate linear arrays with uniformly distributed normals by using delays. The directional responses are compared with the output from an array in an infinite homogenous fluid. These outputs are of interest as they are used to determine the direction of arrival of the plane wave. Numerical results are presented for a circular array with 32 hydrophones and 12 hydrophones in each sector. The problem is of interest because arrays of hydrophones are housed inside sonar domes and acoustic plane waves from distant sources are scattered by the dome filled with fresh water and cause deterioration in the performance of the array.

Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte

Slideshow by POLLYFIBRE

A live work where digital and analogue media collide. This work uses the Internet as a central point of departure in that the script is taken from the Wikipedia entry for the word 'slideshow'. Words are randomly extracted and transferred onto photographic 35mm slide to be projected with analogue carousel slide projectors taking the audience into a visual wordplay, from Google to PowerPoint presentation. The sound of projectors is manipulated gradually into a clashing, confrontational, digital/analogue crescendo. 'Slideshow' investigates how information is sourced, navigated and considered in a culture of accelerating mediation. It posits the notion of a post-digital era in which we are increasingly faced with challenging questions of authenticity and authority.

File Transfer Protocol

The discourse surrounding the virtual has moved away from the utopian thinking accompanying the rise of the Internet in the 1990s. The Cyber-gurus of the last decades promised a technotopia removed from materiality and the confines of the flesh and the built environment, a liberation from old institutions and power structures. But since then, the virtual has grown into a distinct yet related sphere of cultural and political production that both parallels and occasionally flows over into the old world of material objects. The strict dichotomy of matter and digital purity has been replaced more recently with a more complex model where both the world of stuff and the world of knowledge support, resist and at the same time contain each other. Online social networks amplify and extend existing ones; other cultural interfaces like youtube have not replaced the communal experience of watching moving images in a semi-public space (the cinema) or the semi-private space (the family living room). Rather the experience of viewing is very much about sharing and communicating, offering interpretations and comments. Many of the web’s strongest entities (Amazon, eBay, Gumtree etc.) sit exactly at this juncture of applying tools taken from the knowledge management industry to organize the chaos of the material world along (post-)Fordist rationality. Since the early 1990s there have been many artistic and curatorial attempts to use the Internet as a platform of producing and exhibiting art, but a lot of these were reluctant to let go of the fantasy of digital freedom. Storage Room collapses the binary opposition of real and virtual space by using online data storage as a conduit for IRL art production. The artworks here will not be available for viewing online in a 'screen' environment but only as part of a downloadable package with the intention that the exhibition could be displayed (in a physical space) by any interested party and realised as ambitiously or minimally as the downloader wishes, based on their means. The artists will therefore also supply a set of instructions for the physical installation of the work alongside the digital files. In response to this curatorial initiative, File Transfer Protocol invites seven UK based artists to produce digital art for a physical environment, addressing the intersection between the virtual and the material. The files range from sound, video, digital prints and net art, blueprints for an action to take place, something to be made, a conceptual text piece, etc. About the works and artists: Polly Fibre is the pseudonym of London-based artist Christine Ellison. Ellison creates live music using domestic devices such as sewing machines, irons and slide projectors. Her costumes and stage sets propose a physical manifestation of the virtual space that is created inside software like Photoshop. For this exhibition, Polly Fibre invites the audience to create a musical composition using a pair of amplified scissors and a turntable. http://www.pollyfibre.com John Russell, a founding member of 1990s art group Bank, is an artist, curator and writer who explores in his work the contemporary political conditions of the work of art. In his digital print, Russell collages together visual representations of abstract philosophical ideas and transforms them into a post apocalyptic landscape that is complex and banal at the same time. www.john-russell.org The work of Bristol based artist Jem Nobel opens up a dialogue between the contemporary and the legacy of 20th century conceptual art around questions of collectivism and participation, authorship and individualism. His print SPACE concretizes the representation of the most common piece of Unicode: the vacant space between words. In this way, the gap itself turns from invisible cipher to sign. www.jemnoble.com Annabel Frearson is rewriting Mary Shelley's Frankenstein using all and only the words from the original text. Frankenstein 2, or the Monster of Main Stream, is read in parts by different performers, embodying the psychotic character of the protagonist, a mongrel hybrid of used language. www.annabelfrearson.com Darren Banks uses fragments of effect laden Holywood films to create an impossible space. The fictitious parts don't add up to a convincing material reality, leaving the viewer with a failed amalgamation of simulations of sophisticated technologies. www.darrenbanks.co.uk FIELDCLUB is collaboration between artist Paul Chaney and researcher Kenna Hernly. Chaney and Hernly developed together a project that critically examines various proposals for the management of sustainable ecological systems. Their FIELDMACHINE invites the public to design an ideal agricultural field. By playing with different types of crops that are found in the south west of England, it is possible for the user, for example, to create a balanced, but protein poor, diet or to simply decide to 'get rid' of half the population. The meeting point of the Platonic field and it physical consequences, generates a geometric abstraction that investigates the relationship between modernist utopianism and contemporary actuality. www.fieldclub.co.uk Pil and Galia Kollectiv, who have also curated the exhibition are London-based artists and run the xero, kline & coma gallery. Here they present a dialogue between two computers. The conversation opens with a simple text book problem in business studies. But gradually the language, mimicking the application of game theory in the business sector, becomes more abstract. The two interlocutors become adversaries trapped forever in a competition without winners. www.kollectiv.co.uk

A multi-wavelet based technique for calculating dense 2D disparity maps from stereo

A vision based approach for calculating accurate 3D models of the objects is presented. Generally industrial visual inspection systems capable of accurate 3D depth estimation rely on extra hardware tools like laser scanners or light pattern projectors. These tools improve the accuracy of depth estimation but also make the vision system costly and cumbersome. In the proposed algorithm, depth and dimensional accuracy of the produced 3D depth model depends on the existing reference model instead of the information from extra hardware tools. The proposed algorithm is a simple and cost effective software based approach to achieve accurate 3D depth estimation with minimal hardware involvement. The matching process uses the well-known coarse to fine strategy, involving the calculation of matching points at the coarsest level with consequent refinement up to the finest level. Vector coefficients of the wavelet transform-modulus are used as matching features, where wavelet transform-modulus maxima defines the shift invariant high-level features with phase pointing to the normal of the feature surface. The technique addresses the estimation of optimal corresponding points and the corresponding 2D disparity maps leading to the creation of accurate depth perception model.

Depth estimation of metallic objects using multiwavelets scale-space representation

The problem of dimensional defects in aluminum die-castings is widespread throughout the foundry industry and their detection is of paramount importance in maintaining product quality. Due to the unpredictable factory environment and metallic with highly reflective nature, it is extremely hard to estimate true dimensionality of these metallic parts, autonomously. Some existing vision systems are capable of estimating depth to high accuracy, however are very much hardware dependent, involving the use of light and laser pattern projectors, integrated into vision systems or laser scanners. However, due to the reflective nature of these metallic parts and variable factory environments, the aforementioned vision systems tend to exhibit unpromising performance. Moreover, hardware dependency makes these systems cumbersome and costly. In this work, we propose a novel robust 3D reconstruction algorithm capable of reconstructing dimensionally accurate 3D depth models of the aluminum die-castings. The developed system is very simple and cost effective as it consists of only a pair of stereo cameras and a defused fluorescent light. The proposed vision system is capable of estimating surface depths within the accuracy of 0.5mm. In addition, the system is invariant to illuminative variations as well as orientation and location of the objects on the input image space, making the developed system highly robust. Due to its hardware simplicity and robustness, it can be implemented in different factory environments without a significant change in the setup. The proposed system is a major part of quality inspection system for the automotive manufacturing industry.

Lanternfanten

In his work, filmmaker and media artist Dirk de Bruyn deals with the disorientating and traumatic experience of media saturated environments. His perfomance of LanterNfanten for three projectors created an absorbing space where time was disturbed and compressed as a kind of personal research on bodily trauma and cultural qisplacement, employing hand drawn, afterimage, single frame and flicker work. It was accompanied by a live soundtrack from Brisbane based composer Joel Stern, merging music concrete, art brut and noise.

Retinex reflux

Over the last 30 years Melbourne-based film-maker, writer and academic Dirk de Bruyn has made numerous experimental, documentary and animation films and videos. In his first visit to Wellington he presents Retinex Reflux; a live film performance that uses multiple 16mm film projectors in an explosion of light, colour and sound. Described as "explosively anarchic" De Bruyns films are cut-up collages that draw on animation, found footage and fragments of dialogue.

RGB Wattle Park chalet

New technologies have arguably displaced the hegemony of painting within the hierarchies of contemporary art. Projectors and other digital imaging technologies in particular continue to expand the contemporary artist’s aesthetic and conceptual possibilities beyond canvas, paper, and stone. Yet painting - the practice of smearing coloured mud about - far from being superseded, simply continues to cannibalise these powerful technologies extruding them into its own analogue processes. Whether intentionally or as an by-product of this cannibalisation, painting tends to create a critical distance in which the tacit aspects of these technologies – their representational language and ‘special effects’ - are made fully visible. Of course 'easel' painting practices persist not only to critique new technologies. Rather new technologies inevitably fold back into the now souped-up vocabularies of contemporary painting, expanding the medium’s physical boundaries, formal strategies, and modes of display.

YGR Fontainebleau

New technologies have arguably displaced the hegemony of painting in the hierarchies of contemporary art. Projectors and other digital imaging tools in particular continue to expand the artist’s aesthetic and conceptual possibilities beyond canvas, paper, and stone. Yet painting, (the practice of smearing coloured mud about) far from being marginalised, simply continues to cannibalise these new technologies extruding them into its own analogue processes. Whether intentionally or as a by-product of this cannibalisation, painting creates a critical distance in which the tacit aspects of these technologies – their representational language and ‘special effects’ - are made fully visible. Of course ‘traditional’ easel painting practices persist not just to critique new technologies. Digital imaging technologies inevitably feed back into the souped-up vocabularies of contemporary painting, expanding the medium’s physical boundaries, formal strategies, and modes of display. The work for this project explores the ways in which projection and virtual geographical mapping invite new configurations for the practice of landscape painting.

YGR Warrandyte

New technologies have arguably displaced the hegemony of painting in the hierarchies of contemporary art. Projectors and other digital imaging tools in particular continue to expand the artist’s aesthetic and conceptual possibilities beyond canvas, paper, and stone. Yet painting, (the practice of smearing coloured mud about) far from being marginalised, simply continues to cannibalise these new technologies extruding them into its own analogue processes. Whether intentionally or as an by-product of this cannibalisation, painting creates a critical distance in which the tacit aspects of these technologies – their representational language and ‘special effects’ - are made visible. Of course ‘traditional’ easel painting practices persist not just to critique new technologies. Digital imaging technologies inevitably feed back into the souped-up vocabularies of contemporary painting, expanding the medium’s physical boundaries, formal strategies, and modes of display. The work for this project explores the ways in which projection and virtual geographical mapping invite new configurations for the practice of landscape painting.

i1234m

In experimental film-artist Dirk De Bruyn’s work, these gestures of syntactical erasure can be understood as a poetic practice which seeks to grasp preverbal early childhood states – an (inevitably futile) attempt to excise meaning from experiences, before language and its attendant comprehension of the world. De Bruyn attributes this impulse to his early immigration from The Netherlands to Australia, and the confusion he experienced in the consequent liminal space between cultures, identities and languages. His tumultuous performances, which typically begin and end in darkness, combine urgent vocal utterances – hollering, screaming and chanting – with the sumptuous illumination of projected film. De Bruyn’s vocalisations meld with and amplify the images’ blooming fields of colour and intricately layered, hand-animated imagery. At Gertrude, Dirk will perform a new work for three 16mm projectors and voice entitled ‘i1234m’.

Surface-scribed transparency-based microplates

Transparency sheets, which are normally associated with use on overhead projectors, offer lowered costs and high amenability for optical diagnostics in microplate instrumentation. An alternative microplate design in which circles are scribed on the surface of the transparency to create the boundaries to hold the drop in place is investigated here. The 3D profile of the scribed regions obtained optically showed strong likelihood of affecting three-phase contact line interactions. During dispensation, the contact angle (?95°) was larger than the drop advancing state (?80°) due to a period of nonadhesion, where the contact angle later reduced to the drop advancing state followed by increase in the liquid area coverage on the substrate. It was established that 50 ?L was needed to fill the well fully, and the maximum volume retainable before breaching was 190 ?L. While the tilt angle needed for displacement reduced significantly from 50 to 95 ?L, this was markedly better than nonscribed surfaces, where tilt angles always had to be kept to within 30°. It was found that there was greater ability to fill the well with smaller volumes with dispensation at the center. This was attributed to the growing contact line not meeting the scribed edge in parallel if liquid was dispensed closer to it, wherein pinning reduction in some directions permitted liquid travel along the scribed edge to undergo contact angle hysteresis. Fluorescence measurements conducted showed no performance compromise when using scribed transparency microplates over standard microplates.

Night visions

Performance with 3 16mm Projectors and one video projector at Liaison of Independent Filmmakers Toronto, using materials produced in the workshop and the residency. Included was a text spoken in Dutch and English from Abel Tasman's landing on Tasmania's shores during his voyage of expedition.