In this paper, we constrain the dimensionless Compton wavelength parameter $B_0$ of $f(R)$ gravity as well as the mass of sterile neutrino by using the cosmic microwave background observations, the baryon acoustic oscillation surveys, and the linear growth rate measurements. Since both the $f(R)$ model and the sterile neutrino generally predict scale-dependent growth rates, we utilize the growth rate data measured in different wavenumber bins with the theoretical growth rate approximatively scale-independent in each bin. The employed growth rate data come from the peculiar velocity measurements at $z=0$ in five wavenumber bins, and the redshift space distortions measurements at $z=0.25$ and $z=0.37$ in one wavenumber bin. By constraining the $f(R)$ model alone, we get a tight 95% upper limit of $log_{10}B_0<-4.1$. This result is slightly weakened to $log_{10}B_0<-3.8$ (at 2$sigma$ level) once we simultaneously constrain the $f(R)$ model and the sterile neutrino mass, due to the degeneracy between the parameters of the two. For the massive sterile neutrino parameters, we get the effective sterile neutrino mass $m_{ u,{rm{sterile}}}^{rm{eff}}<0.62$ eV (2$sigma$) and the effective number of relativistic species $N_{rm eff}<3.90$ (2$sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{ u,{rm{sterile}}}^{rm{eff}}<0.56$ eV (2$sigma$) and $N_{rm eff}<3.92$ (2$sigma$) in the standard $Lambda$CDM model.
The origin of ultra-compact dwarfs (UCDs)--objects larger and more massive than typical globular clusters (GCs), but more compact than typical dwarf galaxies--has been hotly debated in the 15 years since their discovery. Even whether UCDs should be considered galactic in origin, or simply the most extreme GCs, is not yet settled. We present the dynamical properties of 97 spectroscopically confirmed UCDs (rh >~10 pc) and 911 GCs associated with central cD galaxy of the Virgo cluster, M87. Our UCDs, of which 89% have M_star > ~2X10^6 M_sun and 92% are as blue as the classic blue GCs, nearly triple the sample of previous confirmed Virgo UCDs, providing by far the best opportunity for studying the global dynamics of a UCD system. We found that (1) UCDs have a surface number density profile that is shallower than that of the blue GCs in the inner ~ 70 kpc and as steep as that of the red GCs at larger radii; (2) UCDs exhibit a significantly stronger rotation than the GCs, and the blue GCs seem to have a velocity field that is more consistent with that of the surrounding dwarf ellipticals than with that of UCDs; (3) UCDs have a radially increasing orbital anisotropy profile, and are tangentially-biased at radii < ~ 40 kpc and radially-biased further out. In contrast, the blue GCs become more tangentially-biased at larger radii beyond ~ 40 kpc; (4) GCs with M_star > 2X10^6 M_sun have rotational properties indistinguishable from the less massive ones, suggesting that it is the size, instead of mass, that differentiates UCDs from GCs as kinematically distinct populations. We conclude that most UCDs in M87 are not consistent with being merely the most luminous and extended examples of otherwise normal GCs. The radially-biased orbital structure of UCDs at large radii is in general agreement with the tidally threshed dwarf galaxy scenario.
Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T-Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.
In the probe limit, we numerically construct a holographic p-wave superfluid model in the 4D and 5D AdS black holes coupled to a Maxwell-complex vector field. We find that, for the condensate with the fixed superfluid velocity, the results are similar to the s-wave cases in both 4D and 5D spacetimes. In particular, The Cave of Winds and the phase transition always being the second order take place in the 5D case. Moreover, we find the second-first order translating point $frac{S_y}{mu}$ increases with the mass squared. Furthermore, for the supercurrent with the fixed temperature, the results agree with the GL prediction near the critical temperature. In addition, this complex vector superfluid model is still a generalization of the SU(2) superfluid model, and also provides a holographic realization of the $He_3$ superfluid system.
Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, a systematic method for retrieving the Bethe-type eigenstates of integrable models without obvious reference state is developed by employing certain orthogonal basis of the Hilbert space. With the XXZ spin torus model and the open XXX spin-1/2 chain as examples, we show that for a given inhomogeneous T-Q relation and the associated Bethe Ansatz equations, the constructed Bethe-type eigenstate has a well-defined homogeneous limit.
We propose a mechanism to suppress proton decay induced by dimension-5 operators in a supersymmetric SO(10) model. Proton lifetime is directly connected with the intermediate vacuum expectation value which is responsible for the seesaw mechanism. The model shows many consistencies with the present theoretical results such as the components of the two Higgs doublets in the minimal supersymmetric standard model.
The extended supersymmetric SO(10) model with missing partner mechanism is studied. An intermediate vacuum expectation value is incorporated which corresponds to the see-saw scale. Gauge coupling unification is not broken explicitly. Proton decay is found to satisfy the present experimental limits at the cost of fine-tuning some parameters.
In the model of gauge mediation of SUSY breaking in the presence of tree-level mediation, the Froggatt-Nielsen mechanism provides a different hierarchy of sparticle masses. We study the spectra and show the results to be like those in an effective supersymmetric model.
Cooperative transmission is an emerging communication technique that takes advantage of the broadcast nature of wireless channels. However, due to low spectral efficiency and the requirement of orthogonal channels, its potential for use in future wireless networks is limited. In this paper, by making use of multiuser detection (MUD) and network coding, cooperative transmission protocols with high spectral efficiency, diversity order, and coding gain are developed. Compared with the traditional cooperative transmission protocols with single-user detection, in which the diversity gain is only for one source user, the proposed MUD cooperative transmission protocols have the merit that the improvement of one users link can also benefit the other users. In addition, using MUD at the relay provides an environment in which network coding can be employed. The coding gain and high diversity order can be obtained by fully utilizing the link between the relay and the destination. From the analysis and simulation results, it is seen that the proposed protocols achieve higher diversity gain, better asymptotic efficiency, and lower bit error rate, compared to traditional MUD schemes and to existing cooperative transmission protocols. From the simulation results, the performance of the proposed scheme is near optimal as the performance gap is 0.12dB for average bit error rate (BER) 10^{-6} and 1.04dB for average BER 10^(-3), compared to two performance upper bounds.
Recently, a dark energy model characterized by the age of the universe, dubbed ``agegraphic dark energy, was proposed by Cai. In this paper, a connection between the quintessence scalar-field and the agegraphic dark energy is established, and accordingly, the potential of the agegraphic quintessence field is constructed.
