Perturbations of Single-field Inflation in Modified Gravity Theory

In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form $f(R)$. Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so in despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure $f(R)$ theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there are large parameter space in these models, we show that it is easy to fit the data very well.Comment: 9 pages, 1 figure, substantially improved, matching with the published versio

Disentangle plume-induced anisotropy in the velocity field in buoyancy-driven turbulence

We present a method of disentangling the anisotropies produced by the cliff structures in turbulent velocity field and test it in the system of turbulent Rayleigh-B\'{e}nard (RB) convection. It is found that in the RB system the cliff structures in the velocity field are generated by thermal plumes. These cliff structures induce asymmetry in the velocity increments, which leads us to consider the plus and minus velocity structure functions (VSF). The plus velocity increments exclude cliff structures, while the minus ones include them. Our results show that the scaling exponents of the plus VSFs are in excellent agreement with those predicted for homogeneous and isotropic turbulence (HIT), whereas those of the minus VSFs exhibit significant deviations from HIT expectations in places where thermal plumes abound. These results demonstrate that plus and minus VSFs can be used to quantitatively study the effect of cliff structures in the velocity field and to effectively disentangle the associated anisotropies caused by these structures.Comment: 10 pages, 5 figure

A Search Strategy of Level-Based Flooding for the Internet of Things

This paper deals with the query problem in the Internet of Things (IoT). Flooding is an important query strategy. However, original flooding is prone to cause heavy network loads. To address this problem, we propose a variant of flooding, called Level-Based Flooding (LBF). With LBF, the whole network is divided into several levels according to the distances (i.e., hops) between the sensor nodes and the sink node. The sink node knows the level information of each node. Query packets are broadcast in the network according to the levels of nodes. Upon receiving a query packet, sensor nodes decide how to process it according to the percentage of neighbors that have processed it. When the target node receives the query packet, it sends its data back to the sink node via random walk. We show by extensive simulations that the performance of LBF in terms of cost and latency is much better than that of original flooding, and LBF can be used in IoT of different scales