Orange Peels and Fresnel Integrals

There are two standard ways of peeling an orange: either cut the skin along meridians, or cut it along a spiral. We consider here the second method, and study the shape of the spiral strip, when unfolded on a table. We derive a formula that describes the corresponding flattened-out spiral. Cutting the peel with progressively thinner strip widths, we obtain a sequence of increasingly long spirals. We show that, after rescaling, these spirals tends to a definite shape, known as the Euler spiral. The Euler spiral has applications in many fields of science. In optics, the illumination intensity at a point behind a slit is computed from the distance between two points on the Euler spiral. The Euler spiral also provides optimal curvature for train tracks between a straight run and an upcoming bend. It is striking that it can be also obtained with an orange and a kitchen knife

Inflaton Particles in Reheating

In many theories of reheating starting from the classical spatially homogeneous inflaton field, its accompanying inhomogeneous part (which arises from primordial quantum fluctuations) is treated as a first order perturbation. We examine some consequences of treating it non-perturbatively in a model where a first order treatment is invalid. In particular we consider effects on the long-wavelength curvature parameter relevant to the cosmic microwave background fluctuations.Comment: 14 pages, 4 figures;code corrected,figures and some conclusions change

Topological modular forms and conformal nets

We describe the role conformal nets, a mathematical model for conformal field theory, could play in a geometric definition of the generalized cohomology theory TMF of topological modular forms. Inspired by work of Segal and Stolz-Teichner, we speculate that bundles of boundary conditions for the net of free fermions will be the basic underlying objects representing TMF-cohomology classes. String structures, which are the fundamental orientations for TMF-cohomology, can be encoded by defects between free fermions, and we construct the bundle of fermionic boundary conditions for the TMF-Euler class of a string vector bundle. We conjecture that the free fermion net exhibits an algebraic periodicity corresponding to the 576-fold cohomological periodicity of TMF; using a homotopy-theoretic invariant of invertible conformal nets, we establish a lower bound of 24 on this periodicity of the free fermions

O piano (bem) informado : processos de interiorização e crescimento

Este livro debruça-se sobre questões ligadas à metodologia do piano, incluindo aspectos técnicos, musicais e artísticos, num enquadramento que engloba algumas das principais reflexões éticas, estéticas e filosóficas de referência. O objetivo deste trabalho é a partilha de uma visão baseada na experiência pessoal e profissional na área do piano. Este texto assume uma certa continuidade com as grandes contribuições de autores tais como Ludwig Deppe, Matthay Tobias, Grigory Kogan, Heinrich Neuhaus e George Kochevitsky publicado. Ao mesmo tempo que se integra e complementa alguma dessa literatura especializada, aponta ideias, sugestões e pontos de vista caracterizados pela inovação e aplicabilidade racional e científica

The (well) informed piano: internalization and growth process

The subject matter of this book is about piano methodology, including technical, musical, artistic, ethical and philosophical issues and reflections. The purpose of this work is to share a personal professional experience insight in the field of piano performance. This text assumes a certain continuity to the major contributions of artists like Ludwig Deppe, Tobias Matthay, Grigory Kogan, Heinrich Neuhaus and George Kochevitsky. At the same time, it tries to integrate and complement this selected literature, bringing new ideas and hints to specific professional issues

Chromospheric Inversions of a Micro-flaring Region

We use spectropolarimetric observations of the Ca II 8542~\AA\ line, taken from the Swedish 1-m Solar Telescope (SST), in an attempt to recover dynamic activity in a micro-flaring region near a sunspot via inversions. These inversions show localized mean temperature enhancements of $\sim$1000~K in the chromosphere and upper photosphere, along with co-spatial bi-directional Doppler shifting of 5 - 10 km s$^{-1}$. This heating also extends along a nearby chromospheric fibril, co-spatial to 10 - 15 km s$^{-1}$ down-flows. Strong magnetic flux cancellation is also apparent in one of the footpoints, concentrated in the chromosphere. This event more closely resembles that of an Ellerman Bomb (EB), though placed slightly higher in the atmosphere than is typically observed.Comment: 9 pages, 9 figures, accepted in ApJ. Movies are stored here: https://star.pst.qub.ac.uk/webdav/public/areid/Microflare