Comparing a few distributions of transverse momenta in high energy collisions

Transverse momentum spectra of particles produced in high energy collisions are very important due to their relations to the excitation degree of interacting system. To describe the transverse momentum spectra, one can use more than one probability density functions of transverse momenta, which are simply called the functions or distributions of transverse momenta in some cases. In this paper, a few distributions of transverse momenta in high energy collisions are compared with each other in terms of plots to show some quantitative differences. Meanwhile, in the framework of Tsallis statistics, the distributions of momentum components, transverse momenta, rapidities, and pasudorapidities are obtained according to the analytical and Monte Carlo methods. These analyses are useful to understand carefully different distributions in high energy collisions.Comment: 11 pages, 7 figures. Results in Physics, Accepte

Pilot Power Allocation Through User Grouping in Multi-Cell Massive MIMO Systems

In this paper, we propose a relative channel estimation error (RCEE) metric, and derive closed-form expressions for its expectation $\rm {Exp}_{rcee}$ and the achievable uplink rate holding for any number of base station antennas $M$, with the least squares (LS) and minimum mean squared error (MMSE) estimation methods. It is found that RCEE and $\rm {Exp}_{rcee}$ converge to the same constant value when $M\rightarrow\infty$, resulting in the pilot power allocation (PPA) is substantially simplified and a PPA algorithm is proposed to minimize the average $\rm {Exp}_{rcee}$ per user with a total pilot power budget $P$ in multi-cell massive multiple-input multiple-output systems. Numerical results show that the PPA algorithm brings considerable gains for the LS estimation compared with equal PPA (EPPA), while the gains are only significant with large frequency reuse factor (FRF) for the MMSE estimation. Moreover, for large FRF and large $P$, the performance of the LS approaches to the performance of the MMSE, which means that simple LS estimation method is a very viable when co-channel interference is small. For the achievable uplink rate, the PPA scheme delivers almost the same average achievable uplink rate and improves the minimum achievable uplink rate compared with the EPPA scheme.Comment: 30 pages, 5 figures, submitted to IEEE Transactions on Communication

Chaotic Behaviors of Symbolic Dynamics about Rule 58 in Cellular Automata

The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulli στ-shift rule, which is members of Wolfram’s class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected graph of transition matrices of determinative block systems, we divide determinative block systems into two subsets. In addition, it is shown that rule 58 possesses rich and complicated dynamical behaviors in the space of bi-infinite sequences. Furthermore, we prove that four rules of global equivalence class ε43 of CA are topologically conjugate. We use diagrams to explain the attractors of rule 58, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations, and we find that these attractors are not global attractors. The Lameray diagram is used to show clearly the iterative process of an attractor

Insights into the Coupling of Duplication Events and Macroevolution from an Age Profile of Animal Transmembrane Gene Families

The evolution of new gene families subsequent to gene duplication may be coupled to the fluctuation of population and environment variables. Based upon that, we presented a systematic analysis of the animal transmembrane gene duplication events on a macroevolutionary scale by integrating the palaeontology repository. The age of duplication events was calculated by maximum likelihood method, and the age distribution was estimated by density histogram and normal kernel density estimation. We showed that the density of the duplicates displays a positive correlation with the estimates of maximum number of cell types of common ancestors, and the oxidation events played a key role in the major transitions of this density trace. Next, we focused on the Phanerozoic phase, during which more macroevolution data are available. The pulse mass extinction timepoints coincide with the local peaks of the age distribution, suggesting that the transmembrane gene duplicates fixed frequently when the environment changed dramatically. Moreover, a 61-million-year cycle is the most possible cycle in this phase by spectral analysis, which is consistent with the cycles recently detected in biodiversity. Our data thus elucidate a strong coupling of duplication events and macroevolution; furthermore, our method also provides a new way to address these questions

Thermoresponsive Pickering emulsions stabilized by silica nanoparticles in combination with alkyl polyoxyethylene ether nonionic surfactant

We put forward a simple protocol to prepare thermo-responsive Pickering emulsions. Using hydrophilic silica nanoparticles in combination with a low concentration of alkyl polyoxyethylene monododecyl ether (C12En) nonionic surfactant as emulsifier, oil-in-water (o/w) emulsions can be obtained which are stable at room temperature but demulsified at elevated temperature. The stabilization can be restored once the separated mixture is cooled and re-homogenized, and this stabilization-destabilization behavior can be cycled many times. It is found that the adsorption of nonionic surfactant at the silica nanoparticle-water interface via hydrogen bonding between the oxygen atoms in the polyoxyethylene headgroup and the SiOH groups on particle surfaces at low temperature is responsible for the in situ hydrophobization of the particles rendering them surface-active. De-hydrophobization can be achieved at elevated temperature due to weakening or loss of this hydrogen bonding. The time required for demulsification decreases with increasing temperature and the temperature interval between stabilization and destabilization of the emulsions is affected by the surfactant headgroup length. Experimental evidence including microscopy, adsorption isotherms and three-phase contact angles is provided to support the mechanism

Pressure-induced superconductivity in charge-density-wave compound LaTe2-xSbx (x=0 and 0.4)

Here, we have grown single crystals of LaTe2-xSbx (x=0 and 0.4) with continuously adjustable CDW. High-pressure x-ray diffraction show LaTe2 does not undergo phase transition and keep robust below 40 GPa. In-situ high-pressure electrical measurements show LaTe2-xSbx undergo semiconductor-metal-superconductivity transition at 4.6 and 2.5 GPa, respectively. With the doping of Sb, the highest Tc increases from 4.6 to 6.5 K. Theoretical calculations reveal that the CDW has been completely suppressed and the calculated Tc is about 2.97 K at 4.5 GPa, consistent with the measured value. Then, the pressure-induced superconductivity in LaTe2-xSbx can be explained in the framework of the BCS theory.Comment: 11 pages, 5 figure