Fractal space, cosmic strings and spontaneous symmetry breaking

Argyris, John; Ciubotariu, C.; Matuttis, Hans‐Georg

doi:10.1016/s0960-0779(99)00161-7

Cited by 25 publications

(18 citation statements)

References 55 publications

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“…The five dimensional uplifting of the solution leads to an interesting connection with the results in [14][15][16][17][18]. The equation z 2 = t 2 + 1 may be interpreted as absolute in the cordinates ξ = t/z and η = 1/z, which gives the metric line element (see [14,16] for more details)…”

Section: Further Remarksmentioning

confidence: 75%

On a Petrov-type D solution in Einstein-scalar field theory

Agop

Radu

2006

Gen Relativ Gravit

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Section: Further Remarksmentioning

confidence: 75%

On a Petrov-type D solution in Einstein-scalar field theory

Agop

Radu

2006

Gen Relativ Gravit

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“…Particularly, the independence of this relation on the supercooling degree leads the to the Oldfield's relation; 3) ii) The 1D l-thermal anti-solitons -1D l-thermal solitons modes govern the dendritic branche grows laws. For example, the fact that the primary and the secondary dendritic branches tips are localized on a straight line is a consequence of the relation (19);…”

Section: Discussionmentioning

confidence: 99%

“…Individual vortices vortex streets vortex street Furthermore, the time evolution of the dendritic growth process given by a iterated map of the cn elliptic function shows that this is generated by means of a higher dimensional fractal 19) -see Fig. 7 (its fractal dimension (or HausdorffBesicovitch dimension 17) ) D % 2:005 is greater than the topological one, 17) D % 2).…”

Section: Vortex Pairmentioning

confidence: 98%

Dendritic Morphogenesis by Means of a Fractal

Agop

Ioannou

Luchian³

et al. 2004

Mater. Trans.

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One shows that the dendritic morphogenesis is induced by one-dimensional cnoidal thermal oscillation modes of the solid-liquid interface. Particularly, the one-dimensional l-thermal antisoliton -one-dimensional l-thermal soliton modes imposes laws characterizing dendritic branches growth. One deduces a relation between the dendritic growth speed and the dendritic tip radius that depends on the supercooling degree. Particularly one obtains the Oldsfield's relation. The variation of the fractal dimension with the supercooling degree specifies that the dendritic growth are two-dimensional projections of a higher-dimensional fractal.

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“…This phenomena is known from physics, where it is used to describe the creation and successive annihilations of "virtual" elementary particles (and even the universe), see e.g. [1,53,54].…”

Section: Discussionmentioning

confidence: 99%

The Relevance of Non-generic Events in Scale Space Models

Kuijper

Florack

2002

Computer Vision — ECCV 2002

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In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe and model the behaviour of critical point trajectories when various different types of generic events, viz. annihilations and creations of pairs of spatial critical points, (almost) coincide. Although such events are non-generic in mathematical sense, they are not unlikely to be encountered in practice. Furthermore the behaviour leads to the observation that fine-to-coarse tracking of critical points doesn't suffice, since trajectories can form closed loops in scale space. The modelling of the trajectories include these loops. We apply the theory to an artificial image and a simulated MR image and show the occurrence of the described behaviour.

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Fractal space, cosmic strings and spontaneous symmetry breaking

Cited by 25 publications

References 55 publications

On a Petrov-type D solution in Einstein-scalar field theory

On a Petrov-type D solution in Einstein-scalar field theory

Dendritic Morphogenesis by Means of a Fractal

The Relevance of Non-generic Events in Scale Space Models

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