Related papers: Statistics of ambiguous rotations
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static…
Among asteroids there exist ambiguities in their rotation period determinations. They are due to incomplete coverage of the rotation, noise and/or aliases resulting from gaps between separate lightcurves. To help to remove such…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the…
The axial propagation of circularly polarized light in an optically active structurally chiral medium is exactly solved via full electromagnetic analysis. Some symmetries of the system's characteristic matrix reveal new insights, which are…
We analyze the motion of an overdamped classical particle in a multidimensional periodic potential, driven by a weak external noise. We demonstrate that in steady-state, the presence of temporal correlations in the noise and spatial…
The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the…
A rotation in a Euclidean space V is an orthogonal map on V which acts locally as a plane rotation with some fixed angle. We give a classification of all pairs of rotations in finite-dimensional Euclidean space, up to simultaneous…
We investigate how a symmetric penetrable object immersed in an active fluid becomes motile due to a negative drag acting in the direction of its velocity. While similar phenomena have been reported only for active fluids that posses polar…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…
We derive a necessary condition for the existence of marginally stable circular orbits of test particles in stationary axisymmetric spacetimes which possess a refection symmetry with respect to the equatorial plane; photon orbits are also…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples…
The purpose of this publication is to derive and discuss equations of motion of affinely rigid (homogeneously deformable) body moving in Euclidean space of general dimension $n$. Our aim is to present some analytical methods and to discuss…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…