Related papers: Coordinates based on a magnetic mirror field
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…
Magnetic fields are constrained by the geometry and location of their sources, limiting the ability to freely tailor their spatial distribution. We introduce a general framework to passively convert the magnetic field generated by arbitrary…
We solve "half" the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy force balance. This involves determining which hidden symmetries are admissible as quasisymmetries, and then showing…
In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms.…
Both wire-wound solenoids and cylindrical magnets can be approximately modeled as ideal, azimuthally symmetric solenoids. We present here an exact solution for the magnetic field of an ideal solenoid in an especially easy to use form. The…
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…
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…
We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations we construct an optical map. The expansion of this map gives us the aberration coefficients in…
We show (in a completely analytical and exact manner) that an efficient magnetic field amplification method is operative during the bounce in a time-dependent gauge coupling model. The cosmological magnetic fields so generated have…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
A projective rectangle is like a projective plane that has different lengths in two directions. We develop harmonic conjugation in projective rectangles. We construct projective rectangles in some harmonic matroids (matroids where harmonic…
We suggest a two-dimensional wavelet devised to deduce the large-scale structure of a physical field (e.g., the Galactic magnetic field) from its integrals along straight paths from irregularly spaced data points to a fixed interior point…
The microscopic structure of spin-orbit fields for the technologically important Fe/GaAs interface is uncovered from first principles. A symmetry based method allows to obtain the spin-orbit fields---both their magnitude and…
Suppose we are given an environment consisting of axis-parallel and diagonal line segments with integer endpoints, each of which may be reflective or non-reflective, with integer endpoints, and an initial position for a light ray passing…
Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always…
The problem of the charged-particle motion in an axisymmetric magnetic geometry is used to assess the validity of higher-order Hamiltonian guiding-center theory, which includes higher-order corrections associated with gyrogauge invariance…
A thermodynamic model for the generation of magnetic fields in the planets is proposed, considering crossed effects between gravitational and electric forces. The magnetic field of the Earth is estimated and found to be in agreement with…
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.