1,174 research outputs found
The qualitative behavior at a vortex point for the Chern-Simon-Higgs equation
In this paper, we study the qualitative behavior at a vortex blow-up point
for Chern-Simon-Higgs equation. Roughly speaking, we will establish an energy
identity at a each such point, i.e. the local mass is the sum of the bubbles.
Moreover, we prove that either there is only one bubble which is a singular
bubble or there are more than two bubbles which contains no singular bubble.
Meanwhile, we prove that the energies of these bubbles must satisfy a quadratic
polynomial which can be used to prove the simple blow-up property when the
multiplicity is small. As is well known, for many Liouville type system,
Pohozaev type identity is a quadratic polynomial corresponding to energies
which can be used directly to compute the local mass at a blow-up point. The
difficulty here is that, besides the energy's integration, there is a
additional term in the Pohozaev type identity of Chern-Simon-Higgs equation. We
need some more detailed and delicated analysis to deal with it
Universal theory of spin-momentum-orbital-site locking
Spin textures, i.e., the distribution of spin polarization vectors in
reciprocal space, exhibit diverse patterns determined by symmetry constraints,
resulting in a variety of spintronic phenomena. Here, we propose a universal
theory to comprehensively describe the nature of spin textures by incorporating
three symmetry flavors of reciprocal wavevector, atomic orbital and atomic
site. Such approach enables us to establish a complete classification of spin
textures constrained by the little co-group and predict unprecedentedly
reported spin texture types, such as Zeeman-type spin splitting in
antiferromagnets and quadratic spin texture. To examine the impact of atomic
orbitals and sites, we predict orbital-dependent spin texture and anisotropic
spin-momentum-site locking effects and corresponding material candidates
validated through first-principles calculations. Our theory not only covers all
possible spin textures in crystal solids described by magnetic space groups,
but also introduces new possibilities for designing innovative spin textures by
the coupling of multiple degrees of freedom
Improving Non-Cartesian MRI Reconstruction through Discontinuity Subtraction
Non-Cartesian sampling is widely used for fast magnetic
resonance imaging (MRI). Accurate and fast image reconstruction from
non-Cartesian k-space data becomes a challenge and gains a lot
of attention. Images provided by conventional direct reconstruction
methods usually bear ringing, streaking, and other leakage artifacts
caused by discontinuous structures. In this paper, we tackle these
problems by analyzing the principal point spread function (PSF) of
non-Cartesian reconstruction and propose a leakage reduction
reconstruction scheme based on discontinuity subtraction. Data
fidelity in k-space is enforced during each iteration.
Multidimensional nonuniform fast Fourier transform (NUFFT)
algorithms are utilized to simulate the k-space samples as well as to reconstruct
images. The proposed method is
compared to the direct reconstruction method on computer-simulated
phantoms and physical scans. Non-Cartesian sampling trajectories
including 2D spiral, 2D and 3D radial trajectories are studied. The
proposed method is found useful on reducing artifacts due to high
image discontinuities. It also improves the quality of images
reconstructed from undersampled data
- …