This paper is build around the stationary anisotropic Stokes and Navier-Stokes systems with an $L^infty$-tensor coefficient satisfying an ellipticity condition in terms of symmetric matrices in ${mathbb R}^{ntimes n}$ with zero matrix traces. We anal
yze, in $L^2$-based Sobolev spaces, the non-homogeneous boundary value problems of Dirichlet-transmission type for the anisotropic Stokes and Navier-Stokes systems in a compressible framework in a bounded Lipschitz domain with a Lipschitz interface in ${mathbb R}^n$, $nge 2$ ($n=2,3$ for the nonlinear problems). The transversal interface intersects the boundary of the Lipschitz domain. First, we use a mixed variational approach to prove well-posedness results for the linear anisotropic Stokes system. Then we show the existence of a weak solution for the nonlinear anisotropic Navier-Stokes system by implementing the Leray-Schauder fixed point theorem and using various results and estimates from the linear case, as well as the Leray-Hopf and some other norm inequalities. Explicit conditions for uniqueness of solutions to the nonlinear problems are also provided.
We first present a catalogue of photometric redshifts for 14.68 million galaxies derived from the 7-band photometric data of Hyper Suprime-Cam Subaru Strategic Program and the Wide-field Infrared Survey Explorer using the nearest-neighbour algorithm.
The redshift uncertainty is about 0.024 for galaxies of z<0.7, and steadily increases with redshift to about 0.11 at z~2. From such a large data set, we identify 21,661 clusters of galaxies, among which 5537 clusters have redshifts z>1 and 642 clusters have z>1.5, significantly enlarging the high redshift sample of galaxy clusters. Cluster richness and mass are estimated, and these clusters have an equivalent mass of M_{500} > 0.7*10^{14} Msun. We find that the stellar mass of the brightest cluster galaxies (BCGs) in each richness bin does not significantly evolve with redshift. The fraction of star-forming BCGs increases with redshift, but does not depend on cluster mass.
The ultrafast magnetic dynamics in compensated ferrimagnets not only provides information similar to antiferromagnetic dynamics, but more importantly opens new opportunities for future spintronic devices [Kim et al., Nat. Mater. 16, 1187 (2017)]. One
of the most essential issues for device design is searching for low-power-consuming and high-efficient methods of controlling domain wall. In this work, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to drive the domain wall motion in ferrimagnets. The ultrafast wall motion under the anisotropy gradient is predicted theoretically based on the collective coordinate theory, which is confirmed by the atomistic micromagnetic simulations. The antiferromagnetic spin dynamics is realized at the angular momentum compensation point, and the wall shifting has a constant speed under small gradient and can be slightly accelerated under large gradient due to the broadened wall width during the motion. For nonzero net angular momentum, the Walker breakdown occurs at a critical anisotropy gradient significantly depending on the second anisotropy and interfacial Dzyaloshinkii-Moriya interaction, which is highly appreciated for further experiments including the materials selection and device geometry design. More importantly, this work unveils a low-power-consuming method of controlling the domain wall in ferrimagnets, benefiting to future spintronic applications.
Searching for new methods controlling antiferromagnetic (AFM) domain wall is one of the most important issues for AFM spintronic device operation. In this work, we study theoretically the domain wall motion of an AFM nanowire, driven by the axial ani
sotropy gradient generated by external electric field, allowing the electro control of AFM domain wall motion in the merit of ultra-low energy loss. The domain wall velocity depending on the anisotropy gradient magnitude and intrinsic material properties is simulated based on the Landau-Lifshitz-Gilbert equation and also deduced using the energy dissipation theorem. It is found that the domain wall moves at a nearly constant velocity for small gradient, and accelerates for large gradient due to the enlarged domain wall width. The domain wall mobility is independent of lattice dimension and types of domain wall, while it is enhanced by the Dzyaloshinskii-Moriya interaction. In addition, the physical mechanism for much faster AFM wall dynamics than ferromagnetic wall dynamics is qualitatively explained. This work unveils a promising strategy for controlling the AFM domain walls, benefiting to future AFM spintronic applications.
In this work, we study the rotating magnetic field driven domain wall (DW) motion in antiferromagnetic nanowires, using the micromagnetic simulations of the classical Heisenberg spin model. We show that in low frequency region, the rotating field alo
ne could efficiently drive the DW motion even in the absence of Dzyaloshinskii-Moriya interaction (DMI). In this case, the DW rotates synchronously with the magnetic field, and a stable precession torque is available and drives the DW motion with a steady velocity. In large frequency region, the DW only oscillates around its equilibrium position and cannot propagate. The dependences of the velocity and critical frequency differentiating the two motion modes on several parameters are investigated in details, and the direction of the DW motion can be controlled by modulating the initial phase of the field. Interestingly, a unidirectional DW motion is predicted attributing to the bulk DMI, and the nonzero velocity for high frequency is well explained. Thus, this work does provide useful information for further antiferromagnetic spintronics applications.
By cross-matching the currently largest optical catalog of galaxy clusters and the NVSS radio survey database, we obtain the largest complete sample of brightest cluster galaxies (BCGs) in the redshift range of 0.05<z<0.45, which have radio emission
and redshift information. We confirm that more powerful radio BCGs tend to be these optically very bight galaxies located in more relaxed clusters. We derived the radio luminosity functions of BCGs from the largest complete sample of BCGs, and find that the functions depend on the optical luminosity of BCGs and the dynamical state of galaxy clusters. However, the radio luminosity function does not show significant evolution with redshift.
Diffuse radio emission in galaxy clusters is known to be related to cluster mass and cluster dynamical state. We collect the observed fluxes of radio halos, relics, and mini-halos for a sample of galaxy clusters from the literature, and calculate the
ir radio powers. We then obtain the values of cluster mass or mass proxies from previous observations, and also obtain the various dynamical parameters of these galaxy clusters from optical and X-ray data. The radio powers of relics, halos, and mini-halos are correlated with the cluster masses or mass proxies, as found by previous authors, with the correlations concerning giant radio halos being, in general, the strongest ones. We found that the inclusion of dynamical parameters as the third dimension can significantly reduce the data scatter for the scaling relations, especially for radio halos. We therefore conclude that the substructures in X-ray images of galaxy clusters and the irregular distributions of optical brightness of member galaxies can be used to quantitatively characterize the shock waves and turbulence in the intracluster medium responsible for re-accelerating particles to generate the observed diffuse radio emission. The power of radio halos and relics is correlated with cluster mass proxies and dynamical parameters in the form of a fundamental plane.
Clusters of galaxies have a huge mass which can act as gravitational lenses. Galaxies behind clusters can be distorted to form arcs in images by the lenses. Herein a search was done for giant lensed arcs by galaxy clusters using the SDSS data. By vis
ually inspecting SDSS images of newly identified clusters in the SDSS DR8 and Stripe 82 data, we discover 8 strong lensing clusters together with additional 3 probable and 6 possible cases. The lensed arcs show bluer colors than the member galaxies of clusters. The masses and optical luminosities of galaxy clusters interior to the arcs are calculated, and the mass-to-light ratios are found to be in the range of a few tens of M_Solar/L_Solar, consistent with the distribution of previously known lensing clusters.
We systematically investigate the weakly trapped spin-1 Bose-Einstein condensates with spin-orbit coupling in an external Zeeman field. We find that the mean-field ground state favors either a magnetized standing wave phase or plane wave phase when t
he strength of Zeeman field is below a critical value related to the strength of spin-orbit coupling. Zeeman field can induce the phase transition between standing wave and plane wave phases, and we determine the phase boundary analytically and numerically. The magnetization of these two phases responds to the external magnetic field in a very unique manner, the linear Zeeman effect magnetizes the standing wave phase along the direction of the magnetic field, but the quadratic one demagnetizes the plane wave phase. When the strength of Zeeman field surpasses the critical value, the system is completely polarized to a ferromagnetic state or polar state with zero momentum.
We point out that the widely accepted condition g11g22<g122 for phase separation of a two-component Bose-Einstein condensate is insufficient if kinetic energy is taken into account, which competes against the intercomponent interaction and favors pha
se mixing. Here g11, g22, and g12 are the intra- and intercomponent interaction strengths, respectively. Taking a d-dimensional infinitely deep square well potential of width L as an example, a simple scaling analysis shows that if d=1 (d=3), phase separation will be suppressed as Lrightarrow0 (Lrightarrowinfty) whether the condition g11g22<g122 is satisfied or not. In the intermediate case of d=2, the width L is irrelevant but again phase separation can be partially or even completely suppressed even if g11g22<g122. Moreover, the miscibility-immiscibility transition is turned from a first-order one into a second-order one by the kinetic energy. All these results carry over to d-dimensional harmonic potentials, where the harmonic oscillator length {xi}ho plays the role of L. Our finding provides a scenario of controlling the miscibility-immiscibility transition of a two-component condensate by changing the confinement, instead of the conventional approach of changing the values of the gs.
