Tokamak has toroidal symmetry and symmetry breaking via application of non-axisymmetric field produces disccipation of toroidal momentum by NTV [1] and produces offset toroidal rotation [2]. Callen explained NTV physics and origin of offset toroidal rotation plainly without impurity [3] and with impurity [4]. For impurity, same toroidal rotation for ion and impurity is assumed in [4], which is ...

The toroidal dipole is a peculiar electromagnetic excitation that can not be presented in terms of standard electric and magnetic multipoles. A static toroidal dipole has been shown to lead to violation of parity in atomic spectra and many other unusual electromagnetic phenomena. The existence of electromagnetic resonances of toroidal nature was experimentally demonstrated only recently, first ...

The toroidal response is numerically investigated in a multifold double-ring metamaterials at the antibonding magnetic-dipole mode (i.e., antiparallel magnetic dipoles in one double-ring fold). This intriguing toroidal resonance in metamaterials is considered as a result of the magnetoelectric effect due to the broken balance of the electric near-field environment. We demonstrate that the toroi...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

Ahstract The quantum and classical equations are found which govern the motion of toroidal moments in an external magnetic field. The concrete realization of toroidal moments of higher multipolarities is given, and it is shown how the toroidal moments interact with each other. We recover the 3-dimensional analogue of the Aharonov-Casher effect. It turns out that the toroidal moments should exhi...

Springer 2 This book is a companion to our book [DeDu08], which considered the notions of polycycles, face-regularity and weak face-regularity of plane graphs and toroidal maps. The central actors in the present monograph are the zigzags and central-circuits of 3-or 4-regular plane graphs, which allow to obtain a double covering or covering of the edge-set. This study is mainly focused on speci...

We revisit the fundamental topic of light scattering by single homogenous nanoparticles from the new perspective of excitation and manipulation of toroidal dipoles. It is revealed that besides within all-dielectric particles, toroidal dipoles can also be efficiently excited within homogenous metallic nanoparticles. Moreover, we show that those toroidal dipoles excited can be spectrally tuned th...

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.

We study the toroidality testing and toroidal embedding problems in the context of bounded space algorithms. Specifically, we show that the problem of embedding a toroidal graph on a surface of genus 1 can be solved by an algorithm that runs in deterministic logarithmic space. The algorithm rejects whenever the graph is not toroidal. This algorithm is optimal as we also show a matching hardness...