CAD and creativity: does the computer really help?

We are frequently told by its exponents that computeraided design (CAD) liberates designers and gives them new ways of envisioning their work, but is this really true? CAD in architecture is examined to see to what extent it has enhanced creativity in design. This is partly done by applying a test of creativity advanced by contemporary architect Herman Hertzberger. In this analysis, CAD is found somewhat wanting, and some suggestions are made as to why this might be so

Dequantisation of the Dirac Monopole

Using a sheaf-theoretic extension of conventional principal bundle theory, the Dirac monopole is formulated as a spherically symmetric model free of singularities outside the origin such that the charge may assume arbitrary real values. For integral charges, the construction effectively coincides with the usual model. Spin structures and Dirac operators are also generalised by the same technique.Comment: 22 pages. Version to appear in Proc. R. Soc. London

Minimal kernels of Dirac operators along maps

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma M\otimes_{\mathbb{R}} f^*TN$. To this Dirac operator one can associate an index in $KO^{-dim(M)}(pt)$. If $M$ is $2$-dimensional, one gets a lower bound for the dimension of the kernel of $D^f_{g,h}$ out of this index. We investigate the question whether this lower bound is obtained for generic tupels $(f,g,h)$

The Energy-Momentum tensor on SpincSpin^c manifolds

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spin^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.Comment: To appear in IJGMMP (International Journal of Geometric Methods in Modern Physics), 22 page

Geometric variations of the Boltzmann entropy

We perform a calculation of the first and second order infinitesimal variations, with respect to energy, of the Boltzmann entropy of constant energy hypersurfaces of a system with a finite number of degrees of freedom. We comment on the stability interpretation of the second variation in this framework.Comment: 9 pages, no figure

Dirac lattice

We study the emergence of Dirac fermionic field in the low energy description of non-relativistic dynamical models on graphs admitting continuum limit. The Dirac fermionic field appears as the effective field describing the excitations above point-like Fermi surface. Together with the Dirac fermionic field an effective space-time metric is also emerging. We analyze the conditions for such Fermi points to appear in general, paying special attention to the cases of two and three spacial dimensions.Comment: 26 pages, 4 figures; typo and grammatical corrections, new reference(s) added, version accepted for publicatio

Bi-HKT and bi-Kaehler supersymmetric sigma models

We study CKT (or bi-HKT) N = 4 supersymmetric quantum mechanical sigma models. They are characterized by the usual and the mirror sectors displaying each HKT geometry. When the metric involves isometries, a Hamiltonian reduction is possible. The most natural such reduction with respect to a half of bosonic target space coordinates produces an N = 4 model, related to the twisted Kaehler model due to Gates, Hull and Rocek, but including certain extra F-terms in the superfield action.Comment: 31 pages, minor corrections in the published versio

High power operation of an X-band gyrotwistron

We report the first experimental verification of a gyrotwistron amplifier. The device utilized a single 9.858 GHz, TE011 cavity, a heavily attenuated drift tube, and a long tapered output waveguide section. With a 440 kV, 200-245 A, 1 μs electron beam and a sharply tapered axial magnetic field, peak powers above 21 MW were achieved with a gain near 24 dB. Performance was limited by competition from a fundamental TE11 mode. A multimode code was developed to analyze this system, and simulations were in good agreement with the experiment

Hyperk\"ahler Arnold Conjecture and its Generalizations

We generalize and refine the hyperk\"ahler Arnold conjecture, which was originally established, in the non-degenerate case, for three-dimensional time by Hohloch, Noetzel and Salamon by means of hyperk\"ahler Floer theory. In particular, we prove the conjecture in the case where the time manifold is a multidimensional torus and also establish the degenerate version of the conjecture. Our method relies on Morse theory for generating functions and a finite-dimensional reduction along the lines of the Conley-Zehnder proof of the Arnold conjecture for the torus.Comment: 13 page

Non-commutative Complex Projective Spaces and the Standard Model

The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes' non-commutative geometry and making the complex spaces `fuzzy' a matrix approximation to the fuzzy space allows for three generations to emerge. The generations are associated with three copies of space-time. Higgs' fields and Yukawa couplings can be accommodated in the usual way.Comment: Contribution to conference in honour of A.P. Balachandran's 65th birthday: "Space-time and Fundamental Interactions: Quantum Aspects", Vietri sul Mare, Italy, 25th-31st May, 2003, 10 pages, typset in LaTe