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

Sewerage inflow and infiltration in Universiti Malaysia Pahang (Gambang)

There are several problems occurring during heavy rain which public infrastructure defects will allow unwanted water to enter the sewer system. The sewer pipe system that had cracked or broken causes the excess water from inflow and infiltration to enter the sewer system. This will affect the flow rate and flow capacity of wastewater inside the sewer pipe. The main purpose of this research is to study the inflow and infiltration in the sewerage system by collecting data from field runs in UMP area. Besides, it also studies the relationship of rainfall intensity with inflow and infiltration rate in the sewerage system and to detect whether there are any leakage present in the sewer lines studied which may affect the flow rate in the sewer. This study about sewerage inflow and infiltration in selected sewer in both dry and wet periods, which using the two area velocity flow-meters to measure the sewer flow rate and rainfall data is collected using a rain gauge to achieve the objectives of the research. Thus, the differences between the two periods of inflow and infiltration, and its relationship with rainfall can be clearly seen. This is done on selected sewer line connecting two manholes with no lateral branches in between at Universiti Malaysia Pahang (UMP) area. The result of the inflow and infiltration analysis are compared with the inflow and infiltration rate design limits prescribed in Malaysia Standard MS 1228:1991, previous case studies on inflow and infiltration that carried out in Skudai, Johor and inflow and infiltration estimation range that mention in Hammer & Hammer. The highest infiltration rate that obtained (19.71 liter/day/km/mm-dia) is within the range of design limits prescribed in MS 1228: 1991(50 liter/day/km/mm-dia.) as well as the estimation range that suggested by Hammer & Hammer (18-46 liter/day/km/mm-dia.)

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