515 research outputs found
Multiplicity of closed characteristics on symmetric convex hypersurfaces in
Let be a compact hypersurface in bounding a convex
set with non-empty interior. In this paper it is proved that there always exist
at least geometrically distinct closed characteristics on if
is symmetric with respect to the origin.Comment: 16 page
Emergent Dark Matter in Late Time Universe on Holographic Screen
We discuss a scenario that the dark matter in late time universe emerges as
part of the holographic stress-energy tensor on the hypersurface in higher
dimensional flat spacetime. Firstly we construct a toy model with a de Sitter
hypersurface as the holographic screen in the flat bulk. After adding the
baryonic matter on the screen, we assume that both of the dark matter and dark
energy can be described by the Brown-York stress-energy tensor. From the
Hamiltonian constraint equation in the flat bulk, we find an interesting
relation between the dark matter and baryonic matter's energy density
parameters, by comparing with the Lambda cold dark matter parameterization. We
further compare this holographic embedding of emergent dark matter with
traditional braneworld scenario and present an alternative interpretation as
the holographic universe. It can be reduced to our toy constraint in the late
time universe, with the new parameterization of the Friedmann equation. We also
comment on the possible connection with Verlinde's emergent gravity, where the
dark matter is treated as the elastic response of the baryonic matter on the de
Sitter spacetime background. We show that from the holographic de Sitter model
with elasticity, the Tully-Fisher relation and the dark matter distribution in
the galaxy scale can be derived.Comment: 28 pages, 2 figures; Matches published version and we thank the
referees for many insightful comments; v3: typos in the Friedmann equations
are fixe
Petrov type I Condition and Rindler Fluid in Vacuum Einstein-Gauss-Bonnet Gravity
Recently the Petrov type I condition is introduced to reduce the degrees of
freedom in the extrinsic curvature of a timelike hypersurface to the degrees of
freedom in the dual Rindler fluid in Einstein gravity. In this paper we show
that the Petrov type I condition holds for the solutions of vacuum
Einstein-Gauss-Bonnet gravity up to the second order in the relativistic
hydrodynamic expansion. On the other hand, if imposing the Petrov type I
condition and Hamiltonian constraint on a finite cutoff hypersurface, the
stress tensor of the relativistic Rindler fluid in vacuum Einstein-Gauss-Bonnet
gravity can be recovered with correct first order and second order transport
coefficients.Comment: 25 page
Full Diversity Space-Time Block Codes with Low-Complexity Partial Interference Cancellation Group Decoding
Partial interference cancellation (PIC) group decoding proposed by Guo and
Xia is an attractive low-complexity alternative to the optimal processing for
multiple-input multiple-output (MIMO) wireless communications. It can well deal
with the tradeoff among rate, diversity and complexity of space-time block
codes (STBC). In this paper, a systematic design of full-diversity STBC with
low-complexity PIC group decoding is proposed. The proposed code design is
featured as a group-orthogonal STBC by replacing every element of an Alamouti
code matrix with an elementary matrix composed of multiple diagonal layers of
coded symbols. With the PIC group decoding and a particular grouping scheme,
the proposed STBC can achieve full diversity, a rate of and a
low-complexity decoding for transmit antennas. Simulation results show that
the proposed codes can achieve the full diversity with PIC group decoding while
requiring half decoding complexity of the existing codes.Comment: 10 pages, 3 figures
Multifractal analysis of weighted networks by a modified sandbox algorithm
Complex networks have attracted growing attention in many fields. As a
generalization of fractal analysis, multifractal analysis (MFA) is a useful way
to systematically describe the spatial heterogeneity of both theoretical and
experimental fractal patterns. Some algorithms for MFA of unweighted complex
networks have been proposed in the past a few years, including the sandbox (SB)
algorithm recently employed by our group. In this paper, a modified SB
algorithm (we call it SBw algorithm) is proposed for MFA of weighted
networks.First, we use the SBw algorithm to study the multifractal property of
two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor
dust" WFNs. We also discuss how the fractal dimension and generalized fractal
dimensions change with the edge-weights of the WFN. From the comparison between
the theoretical and numerical fractal dimensions of these networks, we can find
that the proposed SBw algorithm is efficient and feasible for MFA of weighted
networks. Then, we apply the SBw algorithm to study multifractal properties of
some real weighted networks ---collaboration networks. It is found that the
multifractality exists in these weighted networks, and is affected by their
edge-weights.Comment: 15 pages, 6 figures. Accepted for publication by Scientific Report
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