Simulations of the spatial and temporal invariance in the spectra of gradual solar energetic particle events

The spatial and temporal invariance in the spectra of energetic particles in the gradual solar events is reproduced in the simulations. Based on a numerical solution of the focused transport equation, we obtain the intensity time profiles of solar energetic particles (SEPs) accelerated by an interplanetary shock in the three-dimensional interplanetary space. The shock is treated as a moving source of energetic particles with a distribution function. The time profiles of particle flux with different energies are calculated in the ecliptic at $1$ AU. According to our model, we find that shock acceleration strength, parallel diffusion and adiabatic cooling are the main factors in forming the spatial invariance in SEP spectra, and perpendicular diffusion is a secondary factor. In addition, the temporal invariance in SEP spectra is mainly due to the effect of adiabatic cooling. Furthermore, a spectra invariant region, which agrees with observations but is different than the one suggested by Reames and co-workers, is proposed based on our simulations.Comment: Accepted for publication in the Ap

Tau neutrinos from ultracompact dark matter minihalos and constraints on the primordial curvature perturbations

The observations and research on the neutrinos provide a kind of indirect way of revealing the properties of dark matter particles. For the detection of muon neutrinos, the main issue is the large atmospheric background, which is caused by the interactions between the cosmic rays and atoms within the atmosphere. Compared with muon neutrinos, tau neutrinos have a smaller atmospheric background especially for the downward-going direction. Except for the classical neutrino sources, dark matter particles can also annihilate into the neutrinos and are the potential high energy astrophysical sources. The annihilation rate of dark matter particles is proportional to the square of number density; therefore, the annihilation rate is large near the center of dark matter halos especially for the new kind of dark matter structures named ultracompact dark matter minihalos (UCMHs). In previous works, we have investigated the potential muon neutrino flux from UCMHs due to dark matter annihilation. Moreover, since the formation of UCMHs is related to the primordial density perturbations of small scales, we get the constraints on the amplitude of the primordial curvature perturbations of small scales, $1 \lesssim k \lesssim 10^{7} ~\rm Mpc^{-1}$. In this work, we focus on the downward-going tau neutrinos from UCMHs due to dark matter annihilation. Compared with the background of tau neutrino flux we get the constraints on the mass fraction of UCMHs. Then using the limits on the mass fraction of UCMHs we got the constraints on the amplitude of the primordial curvature perturbations which are extended to the scale $k \sim 10^{8} ~ \rm Mpc^{-1}$ compared with previous results.Comment: 10pages, 5figures. comments are welcom

Construction of Minimal Tail-Biting Trellises for Codes over Finite Abelian Groups

A definition of atomic codeword for a group code is presented. Some properties of atomic codewords of group codes are investigated. Using these properties, it is shown that every minimal tail-biting trellis for a group code over a finite abelian group can be constructed from its characteristic generators, which extends the work of Koetter and Vardy who treated the case of a linear code over a field. We also present an efficient algorithm for constructing the minimal tail-biting trellis of a group code over a finite abelian group, given a generator matrix.Comment: 11 pages, submitted to IEEE Transactions on Information Theor

Start-up flow of a viscoelastic fluid in a pipe with fractional Maxwell's model

Unidirectional start-up flow of a viscoelastic fluid in a pipe with fractional Maxwell's model is studied. The flow starting from rest is driven by a constant pressure gradient in an infinite long straight pipe. By employing the method of variable separations and Heaviside operational calculus, we obtain the exact solution, from which the flow characteristics are investigated. It is found that the start-up motion of fractional Maxwell's fluid with parameters $\alpha$ and $\beta$, tends to be at rest as time goes to infinity, except the case of $\beta=1$. This observation, which also can be predicted from the mechanics analogue of fractional Maxwell's model, agrees with the classical work of Friedrich and it indicates fractional Maxwell's fluid presents solid-like behavior if \be\neq 1 and fluid-like behavior if \be=1. For an arbitrary viscoelastic model, a conjecture is proposed to give an intuitive way judging whether it presents fluid-like or solid-like behavior. Also oscillations may occur before the fluid tends to the asymptotic behavior stated above, which is a common phenomenon for viscoelastic fluids.Comment: 14pages, 7 figures. A revised editio

On Picard Type Theorems and Entire Solutions of Differential Equations

We give a connection between the Picard type theorem of Polya-Saxer-Milliox and characterization of entire solutions of a differential equation and then their higher dimensional extensions, which leads further results on both (ordinary and partial) differential equations and Picard type theorems.Comment: 7 page

Baryon productions and collective flow of relativistic heavy-ion collisions in the AGS, SPS, RHIC and LHC energy regions(sNN≤5\sqrt{s_{NN}}\leq5GeV to 5.5 TeV)

The features of net baryon productions and collective flow in relativistic heavy-ion collisions at energies reached at the CERN Large Hadron Collider (LHC), BNL Relativistic Heavy Ion Collider (RHIC), CERN Super Proton Synchrotron (SPS) and BNL Alternating Gradient Synchrotron (AGS) with the model of Non-Uniform Flow Model(NUFM) are systematically studied in this paper. Especially we predict the feature of net baryon productions and collective flow at LHC $\sqrt{s_{NN}}$=5500 GeV basing on the detailed study of that at RHIC $\sqrt{s_{NN}}$=62.4 and 200GeV. The dependencies of the features of baryon stopping and collective flow on the collision energies and centralities are investigated.Comment: 7 pages, 8 figure

Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings

We study the second-order perturbations in the Einstein-de Sitter Universe in synchronous coordinate. We solve the second-order perturbed Einstein equation with scalar-tensor, and tensor-tensor couplings between 1st order perturbations, and obtain, for each coupling, the solutions of scalar, vector, tensor metric perturbations, including both the growing and decaying modes for general initial conditions. We perform general synchronous-to-synchronous gauge transformations up to 2nd order, which are generated by a 1st order vector field and a 2nd order vector field, and obtain all the residual gauge modes of the 2nd order metric perturbations in synchronous coordinates. We show that only the 2nd order vector field is effective for the 2nd order transformations that we consider because the 1st order vector field was already fixed in obtaining the 1st order perturbations. In particular, the 2nd order tensor is invariant under 2nd order gauge transformations using $\xi^{(2)\mu}$ only, just like the 1st order tensor is invariant under 1st order transformations.Comment: 27 pages, 0 figures. Fix some typos of cited formula number from our previous work: typos in the paragraphs below eq.(80), below eq.(88), and below eq.(91). And we make the description above eq.(96) clearer in this updated versio

Transport Protocols in Cognitive Radio Networks: A Survey

Cognitive radio networks (CRNs) have emerged as a promising solution to enhance spectrum utilization by using unused or less used spectrum in radio environments. The basic idea of CRNs is to allow secondary users (SUs) access to licensed spectrum, under the condition that the interference perceived by the primary users (PUs) is minimal. In CRNs, the channel availability is uncertainty due to the existence of PUs, resulting in intermittent communication. Transmission control protocol (TCP) performance may significantly degrade in such conditions. To address the challenges, some transport protocols have been proposed for reliable transmission in CRNs. In this paper we survey the state-of-the-art transport protocols for CRNs. We firstly highlight the unique aspects of CRNs, and describe the challenges of transport protocols in terms of PU behavior, spectrum sensing, spectrum changing and TCP mechanism itself over CRNs. Then, we provide a summary and comparison of existing transport protocols for CRNs. Finally, we discuss several open issues and research challenges. To the best of our knowledge, our work is the first survey on transport protocols for CRNs.Comment: to appear in KSII Transactions on Internet and Information System

Fermion determinant with dynamical chiral symmetry breaking

One -loop fermion determinant is discussed for the case in which dynamical chiral symmetry breaking caused by momentum dependent fermion self energy $\Sigma(p^2)$ take place. The obtained series generalizes the heat kernel expansion for hard fermion mass.Comment: 8 page

Capacity Analysis in Multi-Radio Multi-Channel Cognitive Radio Networks: A Small World Perspective

Cognitive radio (CR) has emerged as a promising technology to improve spectrum utilization. Capacity analysis is very useful in investigating the ultimate performance limits for wireless networks. Meanwhile, with increasing potential future applications for the CR systems, it is necessary to explore the limitations on their capacity in a dynamic spectrum access environment. However, due to spectrum sharing in cognitive radio networks (CRNs), the capacity of the secondary network (SRN) is much more difficult to analyze than that of traditional wireless networks. To overcome this difficulty, in this paper we introduce a novel solution based on small world model to analyze the capacity of SRN. First, we propose a new method of shortcut creation for CRNs, which is based on connectivity ratio. Also, a new channel assignment algorithm is proposed, which jointly considers the available time and transmission time of the channels. And then, we derive the capacity of SRN based on the small world model over multi-radio multi-channel (MRMC) environment. The simulation results show that our proposed scheme can obtain a higher capacity and smaller latency compared with traditional schemes in MRMC CRNs.Comment: Wireless Pers Commun(2014)79:2209-222