Nitsche's method for a Robin boundary value problem in a smooth domain

We prove several optimal-order error estimates for the finite element method applied to an inhomogeneous Robin boundary value problem for the Poisson equation defined in a smooth bounded domain in $\mathbb{R}^n$, $n=2,3$. The boundary condition is imposed weakly by the Nische's method. We also study the symmetric interior penalty discontinuous Galerkin method and prove the same error estimates. Numerical examples to confirmed our results are also reported.Comment: 16 pages, 7 figure

Breaking of Chiral Symmetry and Spontaneous Rotation in a Spinor Bose-Einstein Condensate

We show that a spin-1 Bose-Einstein condensate with ferromagnetic interactions spontaneously generates a topological spin texture, in which the m = \pm 1 components of the magnetic sublevels form vortices with opposite circulations. This phenomenon originates from an interplay between ferromagnetic interactions and spin conservation.Comment: 5 pages, 4 figure

Can Spinor Dipolar Effects be Observed in Bose-Einstein Condensates?

Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of these effects requires magnetic field as low as $\sim 10 \mu$G for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of $\sim 100$ mG. Our scheme enables us to extract genuine dipolar effects and should apply also to $^{52}$Cr BECs.Comment: 4 pages, 3 figure

Einstein--de Haas Effect in Dipolar Bose-Einstein Condensates

The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions -- a phenomenon reminiscent of the Einstein--de Haas effect in ferromagnets.Comment: 4 pages, 4 figures; Final versio