Nonlinear theory of transverse beam echoes

Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough. The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.Comment: 32 pages, 11 figure

Optimization Framework and Graph-Based Approach for Relay-Assisted Bidirectional OFDMA Cellular Networks

This paper considers a relay-assisted bidirectional cellular network where the base station (BS) communicates with each mobile station (MS) using OFDMA for both uplink and downlink. The goal is to improve the overall system performance by exploring the full potential of the network in various dimensions including user, subcarrier, relay, and bidirectional traffic. In this work, we first introduce a novel three-time-slot time-division duplexing (TDD) transmission protocol. This protocol unifies direct transmission, one-way relaying and network-coded two-way relaying between the BS and each MS. Using the proposed three-time-slot TDD protocol, we then propose an optimization framework for resource allocation to achieve the following gains: cooperative diversity (via relay selection), network coding gain (via bidirectional transmission mode selection), and multiuser diversity (via subcarrier assignment). We formulate the problem as a combinatorial optimization problem, which is NP-complete. To make it more tractable, we adopt a graph-based approach. We first establish the equivalence between the original problem and a maximum weighted clique problem in graph theory. A metaheuristic algorithm based on any colony optimization (ACO) is then employed to find the solution in polynomial time. Simulation results demonstrate that the proposed protocol together with the ACO algorithm significantly enhances the system total throughput.Comment: 27 pages, 8 figures, 2 table

Kinetic studies of photo-initiated oxidation of toxic organic pollutants including the formation and the destruction of intermediates

The photo-initiated oxidation process, using hydrogen peroxide or ozone under ultraviolet radiation, has been proven to be an effective treatment method for toxic organic pollutants in wastewater. Most of the recent kinetic studies of the process were concentrated on the breakdown mechanisms of the pollutant itself. The formation and the destruction of intermediates were seldom investigated. Also the mechanisms and their reaction rate constants of free radical formation and destruction in the O3/UV or H2O2/UV reactor were seldom studied. The objective of this research is to study the kinetics of photo-initiated oxidation of toxic organic pollutants including the formation and the destruction of the intermediates. The reaction mechanisms and their rate constants of free radical formation and destruction in the ozone (O3), O3/UV, and H2O2/UV reactor were also studied. Three refractory pollutants, nitrotoluene, naphthalene and 2,4,6-trichlorophenol were conducted in a 120 liter stainless reactor and the ultraviolet radiation source was provided by a low pressure mercury lamp located at the center of the reactor. The analysis of the concentration of pollutants and their intermediates were done by high performance liquid chromatograph (HPLC). The intermediates were identified by the GC/MS and HPLC. The kinetic models developed were verified by the experimental data taken from the reactor. The Rosenbrook Hillclimb Optimization Algorithm together with the Fourth-order Runge-Kutta method were used on a digital computer to calculate the reaction rate constants. By comparing the theoretical output concentration of pollutants with the experimental results in the CSTR processes, it is believed that the calculated rate constants and the proposed kinetic models can be practically used in the photolytic oxidation waste water treatment process