Temperature control in continuous furnace by structural diagram method

The fundamentals of the structural diagram method for distributed parameter systems (DPSs) are presented and reviewed. An example is given to illustrate the application of this method for control design

Probing anisotropic superfluidity of rashbons in atomic Fermi gases

Motivated by the prospect of realizing a Fermi gas of $^{40}$K atoms with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We show that this anisotropic superfluidity can be probed via measuring the momentum distribution and single-particle spectral function in a trapped atomic $^{40}$K cloud near a Feshbach resonance.Comment: 4 pages, 5 figure

Probing Majorana fermions in spin-orbit coupled atomic Fermi gases

We examine theoretically the visualization of Majorana fermions in a two-dimensional trapped ultracold atomic Fermi gas with spin-orbit coupling. By increasing an external Zeeman field, the trapped gas transits from non-topological to topological superfluid, via a mixed phase in which both types of superfluids coexist. We show that the zero-energy Majorana fermion, supported by the topological superfluid and localized at the vortex core, is clearly visible through (i) the core density and (ii) the local density of states, which are readily measurable in experiment. We present a realistic estimate on experimental parameters for ultracold $^{40}$K atoms.Comment: 4 pages, 4 figure

Star 5-edge-colorings of subcubic multigraphs

The star chromatic index of a multigraph $G$, denoted $\chi'_{s}(G)$, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bi-colored. A multigraph $G$ is star $k$-edge-colorable if $\chi'_{s}(G)\le k$. Dvo\v{r}\'ak, Mohar and \v{S}\'amal [Star chromatic index, J Graph Theory 72 (2013), 313--326] proved that every subcubic multigraph is star $7$-edge-colorable, and conjectured that every subcubic multigraph should be star $6$-edge-colorable. Kerdjoudj, Kostochka and Raspaud considered the list version of this problem for simple graphs and proved that every subcubic graph with maximum average degree less than $7/3$ is star list-$5$-edge-colorable. It is known that a graph with maximum average degree $14/5$ is not necessarily star $5$-edge-colorable. In this paper, we prove that every subcubic multigraph with maximum average degree less than $12/5$ is star $5$-edge-colorable.Comment: to appear in Discrete Mathematics. arXiv admin note: text overlap with arXiv:1701.0410