8,000 research outputs found
Decomposition of Optical Flow on the Sphere
We propose a number of variational regularisation methods for the estimation
and decomposition of motion fields on the -sphere. While motion estimation
is based on the optical flow equation, the presented decomposition models are
motivated by recent trends in image analysis. In particular we treat
decomposition as well as hierarchical decomposition. Helmholtz decomposition of
motion fields is obtained as a natural by-product of the chosen numerical
method based on vector spherical harmonics. All models are tested on time-lapse
microscopy data depicting fluorescently labelled endodermal cells of a
zebrafish embryo.Comment: The final publication is available at link.springer.co
Surveying the SO(10) Model Landscape: The Left-Right Symmetric Case
Grand Unified Theories (GUTs) are a very well motivated extensions of the
Standard Model (SM), but the landscape of models and possibilities is
overwhelming, and different patterns can lead to rather distinct
phenomenologies. In this work we present a way to automatise the model building
process, by considering a top to bottom approach that constructs viable and
sensible theories from a small and controllable set of inputs at the high
scale. By providing a GUT scale symmetry group and the field content, possible
symmetry breaking paths are generated and checked for consistency, ensuring
anomaly cancellation, SM embedding and gauge coupling unification. We emphasise
the usefulness of this approach for the particular case of a non-supersymmetric
SO(10) model with an intermediate left-right symmetry and we analyse how
low-energy observables such as proton decay and lepton flavour violation might
affect the generated model landscape.Comment: 36 pages, 6 figure
Compatible orders and fermion-induced emergent symmetry in Dirac systems
We study the quantum multicritical point in a (2+1)-dimensional Dirac system
between the semimetallic phase and two ordered phases that are characterized by
anticommuting mass terms with and symmetry, respectively.
Using expansion around the upper critical space-time dimension of
four, we demonstrate the existence of a stable renormalization-group fixed
point, enabling a direct and continuous transition between the two ordered
phases directly at the multicritical point. This point is found to be
characterized by an emergent symmetry for arbitrary values of
and and fermion flavor numbers , as long as the corresponding
representation of the Clifford algebra exists. Small -breaking
perturbations near the chiral fixed point are therefore irrelevant. This
result can be traced back to the presence of gapless Dirac degrees of freedom
at criticality, and it is in clear contrast to the purely bosonic fixed
point, which is stable only when . As a by-product, we obtain
predictions for the critical behavior of the chiral universality classes
for arbitrary and fermion flavor number . Implications for critical
Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.Comment: 5+2 pages, 1 figure, 1 tabl
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