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We derive the one-dimensional optimal system for a system of three partial differential equations which describe the two-dimensional rotating ideal gas with polytropic parameter $\gamma >2.$ The Lie symmetries and the one-dimensional…
It has long been known to mathematicians and physicists that while a full rotation in three-dimensional Euclidean space causes tangling, two rotations can be untangled. Formally, an untangling is a based nullhomotopy of the double-twist…
We investigate matter collineations of plane symmetric spacetimes when the energy-momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in…
We study differential rotation in late-stage shell convection in a 3D hydrodynamic simulation of a rapidly rotating $16M_\odot$ helium star with a particular focus on the convective oxygen shell. We find that the oxygen shell develops a…
Recently, we have shown the existence of a finite energy one-half monopole. In this paper, we would like to introduce electric charge into the one-half monopole configuration, thus creating a one-half dyon. This one-half dyon possesses…
We construct new geon-type black holes in D>3 dimensions for Einstein's theory coupled to gauge fields. A static nondegenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an…
The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D…
We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…
We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum…
The effective potential energy of the particles in the field of rotating uniformly magnetized celestial body is investigated. The axis of rotation coincides with the axis of the magnetic field. Electromagnetic field of the body is composed…
For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result…
We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edge-to-edge tilings of the sphere by congruent equilateral…
We consider the smallest possible directional reference frames allowed and determine the best one can ever do in preserving quantum information in various scenarios. We find that for the preservation of a single spin state, two orthogonal…
We consider the axially symmetric coupled system of gravitation, electromagnetism and a dilaton field. Reducing from four to three dimensions, the system is described by gravity coupled to a non-linear $\sigma$-model. We find the target…
Rotary-wing flying machines draw attention within the UAV community for their in-place hovering capability, and recently, holonomic motion over fixed-wings. In this paper, we investigate about the power-optimality in a mono-spinner, i.e., a…
We defined several functionals on the set of all triangulations of the finite system of points in d-space achieving global minimum on the Delaunay triangulation (DT). We consider a so called "parabolic" functional and prove it attains its…
Isolated mechanical systems -- e.g., those floating in space, in free-fall, or on a frictionless surface -- are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers…
We study the momentum space representation of energy-momentum tensor two-point functions on a space with a planar boundary in $d=3$. We show that non-conservation of momentum in the direction perpendicular to the boundary allows for new…
The Feynman demonstration that electromagnetic field momentum is real-even for static fields-can be made more pedagogically useful by simplifying its geometry. Instead of Feynman's disk with charged balls on its surface, this article uses…
This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equi-lateral mobile platform and an equilateral-shaped base. Like the other 3-PPPS robots studied in the literature, it is proved that the parallel…