Gravity-based Local Clock Synchronization in Wireless Sensor Networks

Contention-based MAC protocols follow periodic listen/sleep cycles. These protocols face the problem of virtual clustering if different unsynchronized listen/sleep schedules occur in the network, which has been shown to happen in wireless sensor networks. To interconnect these virtual clusters, border nodes maintaining all respective listen/sleep schedules are required. However, this is a waste of energy, if locally a common schedule can be determined. We propose to achieve local synchronization with a mechanism that is similar to gravitation. Clusters represent the mass, whereas synchronization messages sent by each cluster represent the gravitation force of the according cluster. Due to the mutual attraction caused by the clusters, all clusters merge finally. The exchange of synchronization messages itself is not altered by LACAS. Accordingly, LACAS introduces no overhead. Only a not yet used property of synchronization mechanisms is exploited.

Tree-level contribution to B[over ¯]→X_{d}γ using fragmentation functions

We evaluate the most important tree-level contributions connected with the b→uu ¯ ¯ dγ transition to the inclusive radiative decay B ¯ ¯ ¯ →X d γ using fragmentation functions. In this framework the singularities arising from collinear photon emission from the light quarks (u , u ¯ ¯ , and d ) can be absorbed into the (bare) quark-to-photon fragmentation function. We use as input the fragmentation function extracted by the ALEPH group from the two-jet cross section measured at the large electron positron (LEP) collider, where one of the jets is required to contain a photon. To get the quark-to-photon fragmentation function at the fragmentation scale μ F ∼m b , we use the evolution equation, which we solve numerically. We then calculate the (integrated) photon energy spectrum for b→uu ¯ ¯ dγ related to the operators P u 1,2 . For comparison, we also give the corresponding results when using nonzero (constituent) masses for the light quarks.