A transformation linking spherical multipole fields with generalized spheroidal multipole fields is derived. Applications including the inverse diffraction problem for spherically-scanned near field data for sources that due to conformal considerations are efficiently described using spheroidal (either oblate or prolate) volume support regions are discussed with the aid of numerical illustratio...

Conformal field theory (CFT) is important in modern particle physics in various contexts. The most powerful tool in the 2-dimensional CFT is the operator product expansion (OPE). The OPE between the energy-momentum tensor and an operator extracts its conformal weight. We find it interesting to consider the similar issue with respect to the Wilson loop in a conformally invariant Yang-Mills theor...

We generalize the background gauge in the Matrix model to propose a new gauge which is useful for discussing the conformal symmetry. In this gauge, the special conformal transformation (SCT) as the isometry of the near-horizon geometry of the D-particle solution is directly reproduced with the correct coefficient as the quantum correction to the SCT in the Matrix model. We also present a genera...

The self-organization model with a conformal-mapping adaptation is studied in this work. This model is designed to provide conformal transformation to meet the conformality requirement in biological morphology and geometrical surface mapping. This model spans the network field in the input space where topological conformality is preserved. The converged network provides not only the organized c...

We examine crossing probabilities and free energies for conformally invariant critical 2-D systems in rectangular geometries, derived via conformal field theory and Stochastic Löwner Evolution methods. These quantities are shown to exhibit interesting modular behavior, although the physical meaning of modular transformations in this context is not clear. We show that in many cases these functio...

In this paper, two-dimensional turbulent flows in different and complex geometries are simulated by using an accurate grid generation method. In order to analyze the fluid flow, numerical solution of the continuity and Navier-Stokes equations are solved using CFD techniques. Considering the complexity of the physical geometry, conformal mapping is used to generate an orthogonal grid by means of...

I show that Arabidopsis leaf growth can be described with good precision by a conformal map, where expansion is locally isotropic (the same in all directions) but the amount of expansion can vary with position. Data obtained by tracking leaf growth over time can be reproduced with almost 90% accuracy by such a map. The growth follows a Möbius transformation, which is a type of conformal map tha...

The generalization to N=1 superconformal minimal models of the relation between the modular transformation matrix and the fusion rules in rational conformal field theories, the Verlinde theorem, is shown to provide complete information about the fusion rules, including their fermionic parity. The results for the superconformal Tricritical Ising and Ashkin-Teller models agree with the known rati...

We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor ψ of algebraic type F · ψ = 0 with respect to the unique connection ∇ preserving the quasi-Sasakian structure and with totally skew-symmetric torsion. We introduce a certain conformal transformation of almost contact metric manifolds and discuss a link between them and the dilation function i...

The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field and of the gravitational constant. In the present paper the conformal duality is generalized for an arbitrary space-time dimension n 6= 2 and for the general s...