Engineering topics
Dandoloff, Rossen
Publications and source records attributed to Dandoloff, Rossen.
Exact hopfion vortices in a 3D Heisenberg ferromagnet
Here, we find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers n and m. It is a (modified) skyrmion in the z = 0 plane with winding number n, which twists out of the plane m times in the z-direction to become a 3D soliton. Here m arises due to the periodic boundary condition at the z-boundaries. We use Whitehead’s integral expression to find that the Hopf invariant of the soliton is an integer H = nm. It represents a hopfion vortex. Plots of the preimages of this topological soliton show that they are either unknots or nontrivial knots, depending on n and m. Any pair of preimage curves links H times, corroborating the interpretation of H as a linking number. We also calculate the exact energy of the hopfion vortex, and show that its topological lower bound has a sublinear dependence on H. Using Derrick’s scaling analysis, we demonstrate that the presence of a spatial inhomogeneity in the anisotropic interaction, which in turn introduces a characteristic length scale in the system, leads to the stability of the hopfion vortex.
Wormhole as a waveguide for non-relativistic quantum particles
Herein we consider a static wormhole as a waveguide and determine the conditions for full transmission through the wormhole waveguide for a quantum particle satisfying Schrodinger equation. We find that the waveguide is transparent when the angular momentum L of the quantum particle is 0 and for $L\ne 0$ when the de Broglie wavelength of the quantum particle is a multiple depending on the inverse of the angular momentum times the throat radius of the wormhole.