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Using full-wave numerical simulations and analytical multipole expansions we investigated the properties of real-space polarization singularities that emerge in light scattering by subwavelength particles. We considered spherical and torus…
Polarisation states are described by spin expectation values, known as Stokes parameters, whose trajectories in a rotationally symmetric system form a sphere named after Poincar\'e. Here, we show that the trajectories of broken rotational…
It is shown that a simple graph which is embeddable in the real projective plane is minimally 3-rigid if and only if it is (3,6)-tight. Moreover the topologically uncontractible embedded graphs of this type are constructible from one of 8…
We present polarisation observations of five pulsars whose profiles exhibit two distinct emission regions separated by close to 180 degrees of longitude. We fitted the position angle of the linear polarisation using the rotating vector…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
We combine experiments and theory to investigate the orientational dynamics of dipolar ellipsoids, which self-assemble into elongated ribbon-like structures due to the presence in each particle of a permanent magnetic moment perpendicular…
The tidal interaction of a Be star with a binary companion forms two spiral arms that cause orbital modulation of the Be disc structure. The aim of this work is to identify observables in which this modulation is apparent. The structure of…
In algebraic topology, we usually represent surfaces by mean of cellular complexes. This representation is intrinsic, but requires to identify some points through an equivalence relation. On the other hand, embedding a surface in a…
Magnetic fields play important roles in many astrophysical processes. However, there is no universal diagnostic for the magnetic fields in the interstellar medium (ISM) and each magnetic tracer has its limitation. Any new detection method…
Triple orthogonal coordinate systems having coordinate lines as circles or straight lines are considered. Technically, they are represented by trilinear rational quaternionic maps and are called Dupin cyclidic cubes, naturally generalizing…
Transverse photo-induced voltage (TPIV) in 25nm-thick Au film with random holes with 100 nm in diameter is measured for linearly, circularly and elliptically polarized light. By rotating the major axis of ellipse of the light, TPIV exhibits…
Many corner cube prisms, or retroreflectors, employ total internal reflection (TIR) via uncoated rear surfaces. The different elliptical polarization states emerging from the six unique paths through the corner cube complicate the far-field…
We consider the enumeration of tropical curves in M\"obius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces over a complex elliptic curve. Using this correspondence, we…
The two-dimensional surface of a bi-axial ellipsoid is characterized by the lengths of its major and minor axes. Longitude and latitude span an angular coordinate system across. We consider the egg-shaped surface of constant altitude above…
A comparative experimental and theoretical investigation is presented that centres on the effects of structuring black silicon surfaces with linearly, circularly and azimuthally polarized laser pulses under SF6 ambient atmosphere. It is…
We study the formation and dynamics of dipolar rings composed by microscopic ferromagnetic ellipsoids, which self-assemble in water by switching the direction of the applied field. We show how to manipulate these fragile structures and…
A list of galaxies with inner regions revealing polar (or strongly inclined to the main galactic plane) disks and rings is compiled from the literature data. The list contains 47 galaxies of all morphological types, from E to Irr. We…
Topological insulators subject to a time-symmetry-breaking perturbation are predicted to display a magneto-electric effect that causes the electric and magnetic induction fields to mix at the material's surface. This effect induces…
Let $C_{k_1}, \ldots, C_{k_n}$ be cycles with $k_i\geq 2$ vertices ($1\le i\le n$). By attaching these $n$ cycles together in a linear order, we obtain a graph called a polygon chain. By attaching these $n$ cycles together in a cyclic…
We revisit the classification of polarization observables of the cosmic microwave background. There exists a unified approach to the $3 \times 3$ density matrix by which intensity, linear and circular polarization are treated on an equal…