Mobile Phone Faraday Cage

A Faraday cage is an interesting physics phenomena where an electromagnetic wave can be excluded from a volume of space by enclosure with an electrically conducting material. The practical application of this in the classroom is to block the signal to a mobile phone by enclosing it in a metal can! The background of the physics behind this is described in some detail followed by a explanation of some demonstrations and experiments which I have used

Exact solution for random walks on the triangular lattice with absorbing boundaries

The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.Comment: 10 pages, Latex, IOP macro

Equation of the field lines of an axisymmetric multipole with a source surface

Optical spectropolarimeters can be used to produce maps of the surface magnetic fields of stars and hence to determine how stellar magnetic fields vary with stellar mass, rotation rate, and evolutionary stage. In particular, we now can map the surface magnetic fields of forming solar-like stars, which are still contracting under gravity and are surrounded by a disk of gas and dust. Their large scale magnetic fields are almost dipolar on some stars, and there is evidence for many higher order multipole field components on other stars. The availability of new data has renewed interest in incorporating multipolar magnetic fields into models of stellar magnetospheres. I describe the basic properties of axial multipoles of arbitrary degree ℓ and derive the equation of the field lines in spherical coordinates. The spherical magnetic field components that describe the global stellar field topology are obtained analytically assuming that currents can be neglected in the region exterior to the star, and interior to some fixed spherical equipotential surface. The field components follow from the solution of Laplace’s equation for the magnetostatic potential

Carving out OPE space and precise O(2) model critical exponents

We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment

Critical temperature oscillations in magnetically coupled superconducting mesoscopic loops

We study the magnetic interaction between two superconducting concentric mesoscopic Al loops, close to the superconducting/normal phase transition. The phase boundary is measured resistively for the two-loop structure as well as for a reference single loop. In both systems Little-Parks oscillations, periodic in field are observed in the critical temperature Tc versus applied magnetic field H. In the Fourier spectrum of the Tc(H) oscillations, a weak 'low frequency' response shows up, which can be attributed to the inner loop supercurrent magnetic coupling to the flux of the outer loop. The amplitude of this effect can be tuned by varying the applied transport current.Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev.

Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization

We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller

Ruled Laguerre minimal surfaces

A Laguerre minimal surface is an immersed surface in the Euclidean space being an extremal of the functional \int (H^2/K - 1) dA. In the present paper, we prove that the only ruled Laguerre minimal surfaces are up to isometry the surfaces R(u,v) = (Au, Bu, Cu + D cos 2u) + v (sin u, cos u, 0), where A, B, C, D are fixed real numbers. To achieve invariance under Laguerre transformations, we also derive all Laguerre minimal surfaces that are enveloped by a family of cones. The methodology is based on the isotropic model of Laguerre geometry. In this model a Laguerre minimal surface enveloped by a family of cones corresponds to a graph of a biharmonic function carrying a family of isotropic circles. We classify such functions by showing that the top view of the family of circles is a pencil.Comment: 28 pages, 9 figures. Minor correction: missed assumption (*) added to Propositions 1-2 and Theorem 2, missed case (nested circles having nonempty envelope) added in the proof of Pencil Theorem 4, missed proof that the arcs cut off by the envelope are disjoint added in the proof of Lemma

Spin 1 fields in Riemann-Cartan space-times "via" Duffin-Kemmer-Petiau theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.Comment: 8 pages, no figures, revtex. Dedicated to Professor Gerhard Wilhelm Bund on the occasion of his 70th birthday. To appear in Gen. Rel. Grav. Equations numbering corrected. References update