18,018 research outputs found
Finite Element Methods For Interface Problems On Local Anisotropic Fitting Mixed Meshes
A simple and efficient interface-fitted mesh generation algorithm is
developed in this paper. This algorithm can produce a local anisotropic fitting
mixed mesh which consists of both triangles and quadrilaterals near the
interface. A new finite element method is proposed for second order elliptic
interface problems based on the resulting mesh. Optimal approximation
capabilities on anisotropic elements are proved in both the and
norms. The discrete system is usually ill-conditioned due to anisotropic and
small elements near the interface. Thereupon, a multigrid method is presented
to handle this issue. The convergence rate of the multigrid method is shown to
be optimal with respect to both the coefficient jump ratio and mesh size.
Numerical experiments are presented to demonstrate the theoretical results
Scheme to Achieve Silicon Topological Photonics
We derive in the present work topological photonic states purely based on
silicon, a conventional dielectric material, by deforming a honeycomb lattice
of silicon cylinders into a triangular lattice of cylinder hexagons. The
photonic topology is associated with a pseudo time reversal (TR) symmetry
constituted by the TR symmetry respected in general by the Maxwell equations
and the crystal symmetry upon design, which renders the Kramers doubling
in the present photonic system with the role of pseudo spin played by the
circular polarization of magnetic field in the transverse magnetic mode. We
solve Maxwell equations, and demonstrate new photonic topology by revealing
pseudo spin-resolved Berry curvatures of photonic bands and helical edge states
characterized by Poynting vectors.Comment: 5 pages, 5 figure
Topological Properties of Electrons in Honeycomb Lattice with Kekul\'{e} Hopping Textures
Honeycomb lattice can support electronic states exhibiting Dirac energy
dispersion, with graphene as the icon. We propose to derive nontrivial topology
by grouping six neighboring sites of honeycomb lattice into hexagons and
enhancing the inter-hexagon hopping energies over the intra-hexagon ones. We
reveal that this manipulation opens a gap in the energy dispersion and drives
the system into a topological state. The nontrivial topology is characterized
by the index associated with a pseudo time-reversal symmetry
emerging from the symmetry of the Kekul\'{e} hopping texture, where the
angular momentum of orbitals accommodated on the hexagonal "artificial atoms"
behaves as the pseudospin. The size of topological gap is proportional to the
hopping-integral difference, which can be larger than typical spin-orbit
couplings by orders of magnitude and potentially renders topological electronic
transports available at high temperatures.Comment: 7 pages, 7 figure
The Weyl Integration Model for KAK decomposition of Reductive Lie Group
The Weyl integration model presented by An and Wang can be effectively used
to reduce the integration over -space. In this paper, we construct an
especial Weyl integration model for KAK decomposition of Reductive Lie Group
and obtain an integration formula which implies that the integration of
-integrable function over reductive Lie group can be carried out by
first integrating over each conjugacy class and then integrating over the set
of conjugacy classes.Comment: 10 page
Unstable Entropies and Variational Principle for Partially Hyperbolic Diffeomorphisms
We study entropies caused by the unstable part of partially hyperbolic
systems. We define unstable metric entropy and unstable topological entropy,
and establish a variational principle for partially hyperbolic diffeomorphsims,
which states that the unstable topological entropy is the supremum of the
unstable metric entropy taken over all invariant measures. The unstable metric
entropy for an invariant measure is defined as a conditional entropy along
unstable manifolds, and it turns out to be the same as that given by
Ledrappier-Young, though we do not use increasing partitions. The unstable
topological entropy is defined equivalently via separated sets, spanning sets
and open covers along a piece of unstable leaf, and it coincides with the
unstable volume growth along unstable foliation. We also obtain some properties
for the unstable metric entropy such as affineness, upper semi-continuity and a
version of Shannon-McMillan-Breiman theorem
A 28/37/39GHz Multiband Linear Doherty Power Amplifier in Silicon for 5G Applications
This paper presents the first multiband mm-wave linear Doherty PA in silicon
for broadband 5G applications. We introduce a new transformer-based on-chip
Doherty power combiner, which can reduce the impedance transformation ratio in
power back-off (PBO) and thus improve the bandwidth and power-combining
efficiency. We also devise a "driver-PA co-design" method, which creates
power-dependent uneven feeding in the Doherty PA and enhances the Doherty
operation without any hardware overhead or bandwidth compromise. For the proof
of concept, we implement a 28/37/39-GHz PA fully integrated in a standard
130-nm SiGe BiCMOS process, which occupies 1.8mm2. The PA achieves a 52% -3-dB
small-signal S21 bandwidth and a 40% -1-dB large-signal saturated output power
(Psat) bandwidth. At 28/37/39GHz, the PA achieves +16.8/+17.1/+17-dBm Psat,
+15.2/+15.5/+15.4-dBm P1dB, and superior 1.72/1.92/1.62 times efficiency
enhancement over class-B operation at 5.9/6/6.7-dB PBO. Moreover, the PA
demonstrates multi-Gb/s data rates with excellent efficiency and linearity for
64QAM in all the three 5G bands. This PA advances the state of the art for
Doherty, wideband, and 5G silicon PAs in mm-wave bands. It supports drop-in
upgrade for current PAs in existing mm-wave systems and opens doors to compact
system solutions for future multiband 5G massive MIMO and phased-array
platforms
An Algorithm for Deciding the Summability of Bivariate Rational Functions
Let and
be the difference operators with respect to and . A rational function
is called summable if there exist rational functions and
such that . Recently, Chen
and Singer presented a method for deciding whether a rational function is
summable. To implement their method in the sense of algorithms, we need to
solve two problems. The first is to determine the shift equivalence of two
bivariate polynomials. We solve this problem by presenting an algorithm for
computing the dispersion sets of any two bivariate polynomials. The second is
to solve a univariate difference equation in an algebraically closed field. By
considering the irreducible factorization of the denominator of in a
general field, we present a new criterion which requires only finding a
rational solution of a bivariate difference equation. This goal can be achieved
by deriving a universal denominator of the rational solutions and a degree
bound on the numerator. Combining these two algorithms, we can decide the
summability of a bivariate rational function.Comment: 18 page
Convergence rates in the law of large numbers under sublinear expectations
In this note, we study convergence rates in the law of large numbers for
independent and identically distributed random variables under sublinear
expectations. We obtain a strong -convergence version and a strongly quasi
sure convergence version of the law of large numbers.Comment: 12 page
Matrix Linear Discriminant Analysis
We propose a novel linear discriminant analysis approach for the
classification of high-dimensional matrix-valued data that commonly arises from
imaging studies. Motivated by the equivalence of the conventional linear
discriminant analysis and the ordinary least squares, we consider an efficient
nuclear norm penalized regression that encourages a low-rank structure.
Theoretical properties including a non-asymptotic risk bound and a rank
consistency result are established. Simulation studies and an application to
electroencephalography data show the superior performance of the proposed
method over the existing approaches
Quantum Anomalous Hall Effect in a Perovskite and Inverse-Perovskite Sandwich Structure
Based on first-principles calculations, we propose a sandwich structure
composed of a G-type anti-ferromagnetic (AFM) Mott insulator LaCrO grown
along the [001] direction with one atomic layer replaced by an
inverse-perovskite material SrPbO. We show that the system is in a
topologically nontrivial phase characterized by simultaneous nonzero charge and
spin Chern numbers, which can support a spin-polarized and dissipationless edge
current in a finite system. Since these two materials are stable in bulk and
match each other with only small lattice distortions, the composite material is
expected easy to synthesize.Comment: 4 pages, 4 figure
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