Knots, links, anyons and statistical mechanics of entangled polymer rings

The field theory approach to the statistical mechanics of a system of N polymer rings linked together is extended to the case of links whose paths in space are characterized by a fixed number 2s of maxima and minima. Such kind of links are called 2s-plats and appear for instance in the DNA of living organisms or in the wordlines of quasiparticles associated with vortices nucleated in a quasi-two-dimensional superfluid. The path integral theory describing the statistical mechanics of polymers subjected to topological constraints is mapped here into a field theory of quasiparticles (anyons). In the particular case of s=2, it is shown that this field theory admits vortex solutions with special self-dual points in which the interactions between the vortices vanish identically. The topological states of the link are distinguished using two topological invariants, namely the Gauss linking number and the so-called bridge number which is related to s. The Gauss linking number is a topological invariant that is relatively weak in distinguishing the different topological configurations of a general link. The addition of topological constraints based on the bridge number allows to get a glimpse into the non-abelian world of quasiparticles, which is relevant for important applications like topological quantum computing and high-TC superconductivity. At the end an useful connection with the cosh-Gordon equation is shown in the case s=2. © 201

Finding the Origin of the Pioneer Anomaly

Analysis of radio-metric tracking data from the Pioneer 10/11 spacecraft at distances between 20 - 70 astronomical units (AU) from the Sun has consistently indicated the presence of an anomalous, small, constant Doppler frequency drift. The drift can be interpreted as being due to a constant acceleration of a_P= (8.74 \pm 1.33) x 10^{-8} cm/s^2 directed towards the Sun. Although it is suspected that there is a systematic origin to the effect, none has been found. As a result, the nature of this anomaly has become of growing interest. Here we present a concept for a deep-space experiment that will reveal the origin of the discovered anomaly and also will characterize its properties to an accuracy of at least two orders of magnitude below the anomaly's size. The proposed mission will not only provide a significant accuracy improvement in the search for small anomalous accelerations, it will also determine if the anomaly is due to some internal systematic or has an external origin. A number of critical requirements and design considerations for the mission are outlined and addressed. If only already existing technologies were used, the mission could be flown as early as 2010.Comment: 21 SS pages, 4+1 figures. final changes for publicatio

Distributed Clustering in Cognitive Radio Ad Hoc Networks Using Soft-Constraint Affinity Propagation

Absence of network infrastructure and heterogeneous spectrum availability in cognitive radio ad hoc networks (CRAHNs) necessitate the self-organization of cognitive radio users (CRs) for efficient spectrum coordination. The cluster-based structure is known to be effective in both guaranteeing system performance and reducing communication overhead in variable network environment. In this paper, we propose a distributed clustering algorithm based on soft-constraint affinity propagation message passing model (DCSCAP). Without dependence on predefined common control channel (CCC), DCSCAP relies on the distributed message passing among CRs through their available channels, making the algorithm applicable for large scale networks. Different from original soft-constraint affinity propagation algorithm, the maximal iterations of message passing is controlled to a relatively small number to accommodate to the dynamic environment of CRAHNs. Based on the accumulated evidence for clustering from the message passing process, clusters are formed with the objective of grouping the CRs with similar spectrum availability into smaller number of clusters while guaranteeing at least one CCC in each cluster. Extensive simulation results demonstrate the preference of DCSCAP compared with existing algorithms in both efficiency and robustness of the clusters

Number of states for nucleons in a single-jj shell

In this paper we obtain number of states with a given spin $I$ and a given isospin $T$ for systems with three and four nucleons in a single-$j$ orbit, by using sum rules of six-$j$ and nine-$j$ symbols obtained in earlier works.Comment: to be published in Physical Review