One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential

By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.Comment: 6 pages, 3 figure

Controlled mobility in stochastic and dynamic wireless networks

We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of Θ([1 over 1−ρ]) with the system load ρ, in contrast to the Θ([1 over (1−ρ)[superscript 2]]) delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.National Science Foundation (U.S.) (Grant CNS-0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238