The geometrical approach to phase transitions is illustrated by simulating the hightemperature representation of the Ising model on a square lattice.

A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew, for constructions of dynamics on general algebroids. One obtains formalisms similar to the Lagrangian and the Hamiltonian ones. In contrast with recently studied concepts of Analytical Mechanics on Lie algebroids, this approach requires much less than the presence of a Lie algebroid structure on a vector bundle, but i...

The object of this talk is to illustrate the usefulness of symplectic geometry in understanding new features of geometrical optics for spinning light in refractive media, e.g., the subtle transverse shift of light beams across an interface, which has been coined the Spin Hall Effect of Light [1]. We reformulate Fermat’s principle to describe spinning light rays in Riemannian three-manifolds, (M...

We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Due to the fact that the mass of this geometrical tachyon field is √ 2/k times smaller than the corresponding open-string tachyon mass, we find that the slow r...

We consider a substitutive version of the Arnoux-Yoccoz Interval Exchange Transformation (IET) related to the Tribonacci substitution. We construct the so-called stepped lines associated to the fixed points of the substitution in the Abelianisation (symbolic) space. We analyse various projections of the stepped line recovering the Rauzy Fractal, a Peano Curve related to the work of Arnoux [1], ...

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.

The article is dealing with novel and relatively complex computer system for automatic creation of human tissues geometrical models. Applications of the created models can be found in orthopedy, aesthetic surgery, dental surgery, etc. On the input are discrete volume CT/MR data in DICOM 3.0 data format. The models creation process consist of several steps: tissue segmentation, volume data vecto...

The thesis studies the following problem: Given a set of geometrical figures (such as planar polygons), each one labelled according to whether or not it resembles some "ideal" figure, find a good approximation to that ideal figure which can be used to classify other figures in the same way. We work within the PAC learning model introduced by Valiant in 1984. Informally, the concepts under consi...

We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.

This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current require...