Interaction of Charged 3D Soliton with Coulomb Center

The Einstein - de Broglie particle-soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. In the framework of Synge model for interacting scalar and electromagnetic fields a system of integral equations has been obtained, which describes the interaction between charged 3D soliton and Coulomb center. The asymptotic expressions for physical fields, describing soliton moving around the fixed Coulomb center, have been obtained with the help of integral equations. It is shown that the electron-soliton center travels along some stationary orbit around the Coulomb center. The electromagnetic radiation is absent as the Poynting vector has non-wave asymptote $O(r^{-3})$ after averaging over angles, i.e. the existence of spherical surface corresponding to null Poynting vector stream, has been proved. Vector lines for Poynting vector are constructed in asymptotical area.Comment: LaTeX ,12 page

1-Methyl-3-(4-chloro­benzo­yl)imidazo[1,2-a]pyridin-1-ium-2-olate

In the mol­ecule of the title compound, C15H11ClN2O2, the nine-membered heterobicycle is approximately planar [largest deviation from least-squares plane = 0.012 (2) Å] and forms a dihedral angle of 51.14 (8)° with the plane of the 4-chloro­phenyl group. There is a non-classical intra­molecular hydrogen bond between the pyridine α-H atom and the O atom of the benzoyl group. The crystal structure is stabilized by weak C—H⋯O and C—H⋯Cl inter­actions involving the ‘olate’ O atom and the Cl atom attached to the benzoyl group as acceptors

New type of stable particle like states in chiral magnets (Chiral bobbers)

We present a new type of a thermodynamically stable magnetic state at interfaces and surfaces of chiral magnets. The state is a soliton solution of micromagnetic equations localized in all three dimensions near a boundary and contains a singularity, but nevertheless has a finite energy. Both features combine to a quasi-particle state for which we expect unusual transport and dynamical properties. It exhibits high thermal stability and thereby can be considered as promising object for fundamental research and practical applications in spintronic devices. We provide arguments that such a state can be found in different B20-type alloys e.g. Mn$_{1-x}$Fe$_x$Ge, Mn$_{1-x}$Fe$_x$Si, Fe$_{1-x}$Co$_x$Si.Comment: accepted in PR

Variational principles of micromagnetics revisited

We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically non-local. Under minimal assumptions, we establish three distinct variational principles for the stray field energy: a minimax principle involving magnetic scalar potential and two minimization principles involving magnetic vector potential. We then apply our formulations to the dimension reduction problem for thin ferromagnetic shells of arbitrary shapes