Related papers: How does a heavy symmetric top rise?
The interactions of gravitons with spin-1 matter are calculated in parallel with the well known photon case. It is shown that graviton scattering amplitudes can be factorized into a product of familiar electromagnetic forms, and cross…
This paper concerns the structural stability of smooth cylindrical symmetric transonic flows in a concentric cylinder under helically symmetric perturbation of suitable boundary conditions. The deformation-curl decomposition developed by…
The observed alignment of spots in the x-ray films in cosmic ray emulsion experiments is analyzed and interpreted in the framework of geometrical approach. It is shown that the high degree of alignment can appear partly due to the selection…
We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…
A generalization of highly symmetric frames is presented by considering also projective stabilizers of frame vectors. This allows construction of highly symmetric line systems and study of highly symmetric frames in a more unified manner.…
We define the tangent Euler top in General Relativity through a constrained Lagrangian on the orthonormal frame bundle. The corresponding motions are studied to various degrees of approximation, the lowest of which is shown to yield the…
Several problems which could be thought of as belonging to recreational mathematics are described. They are all such that solutions to the problem depend on finding rational points on elliptic curves. Many of the problems considered lead to…
The main issues of the original Symmetrical smoothing method consists of approximation of the extremal volume of the set by the smooth symmetric function (sum of step functions) and then solve the optimization problem. when making…
We study the supremum of the volume of hyperbolic polyhedra with some fixed combinatorics and with vertices of any kind (real, ideal or hyperideal). We find that the supremum is always equal to the volume of the rectification of the…
Flying snakes use a unique method of aerial locomotion: they jump from tree branches, flatten their bodies and undulate through the air to produce a glide. The shape of their body cross-section during the glide plays an important role in…
A new equation is proposed to explain the curvature of spent sparklers. We found the state of a segment of the sparkler to depend strongly on the state of its spent segments. The equation is nearly able to produce the sparkler shape for a…
This work develops a curvature-based geometric formulation of the Euler-Poisson equations by lifting the dynamics to the 3-sphere S^3 equipped with the left-invariant metric induced by the inertia tensor. For the inertia ratio I = (2,2,1)…
Analytical perturbations of the Euler top are considered. The perturbations are based on the Poisson structure for such a dynamical system, in such a way that the Casimir invariants of the system remain invariant for the perturbed flow. By…
Comparative study of topological charge is performed. Topological charges are measured by a cloverleaf operator on smoothed gauge configurations. Various types of smoothing techniques are employed. Agreement of topological charges in…
Flapping animal flight is often modeled as a combined pitching and heaving motion in order to investigate the unsteady flow structures and resulting forces that could augment the animal's lift and propulsive capabilities. This work isolates…
Floating of bodies heavier than the supporting liquid is discussed. Floating of cylindrical, ellipsoidal bodies and rectangular plates possessing lateral dimensions smaller than the capillary length is treated. It is demonstrated that more…
When a falling jet of fluid strikes a horizontal fluid layer, a hydraulic jump arises downstream of the point of impact provided a critical flow rate is exceeded. We here examine a phenomenon that arises below this jump threshold, a…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and…
With the next start of LHC, a huge production of top quarks is expected. There are several models that predict the existence of heavy colored resonances decaying to top quarks in the TeV energy range. A peak in the differential cross…