Short versus long range interactions and the size of two-body weakly bound objects

Very weakly bound systems may manifest intriguing "universal" properties, independent of the specific interaction which keeps the system bound. An interesting example is given by relations between the size of the system and the separation energy, or scaling laws. So far, scaling laws have been investigated for short-range and long-range (repulsive) potentials. We report here on scaling laws for weakly bound two-body systems valid for a larger class of potentials, i.e. short-range potentials having a repulsive core and long-range attractive potentials. We emphasize analogies and differences between the short- and the long-range case. In particular, we show that the emergence of halos is a threshold phenomenon which can arise when the system is bound not only by short-range interactions but also by long-range ones, and this for any value of the orbital angular momentum $\ell$. These results enlarge the image of halo systems we are accustomed to.Comment: 6 pages, 1 figure. To be published in the Proceedings of the Workshop "Hirschegg 2003: Nuclear Structure and Dynamics at the Limits", Hirschegg, January 12 - 18, 200

A New Application of Transient Recorder to Magnetic Measurements (Part I: Core Loss Measurement at Very Low Frequencies)

A new method have been developed based upon analogue-to-digital conversion techniques and memories. The method involves the scaling of operating frequency from "real" to "optimum" for the power loss measurement. The advantages of using this techniques are as follows: (1) extreme availability at lower frequency region, (2) high accuracy and high stability, (3) simple measuring procedure, (4) digital indication. This method can be measured the power losses over the frequency range 0.1Hz to 1kHz for magnetic circuit and d.c. to 1kHz in such a purely resistive circuit. We estimate the accuracy of this core loss measuring system within 1.0% over all these frequency range. Using this system, specific core losses of the various grades of silicon iron have been measured in the frequency range 0.1Hz to 200Hz

Flat Cellular (UMTS) Networks

Traditionally, cellular systems have been built in a hierarchical manner: many specialized cellular access network elements that collectively form a hierarchical cellular system. When 2G and later 3G systems were designed there was a good reason to make system hierarchical: from a cost-perspective it was better to concentrate traffic and to share the cost of processing equipment over a large set of users while keeping the base stations relatively cheap. However, we believe the economic reasons for designing cellular systems in a hierarchical manner have disappeared: in fact, hierarchical architectures hinder future efficient deployments. In this paper, we argue for completely flat cellular wireless systems, which need just one type of specialized network element to provide radio access network (RAN) functionality, supplemented by standard IP-based network elements to form a cellular network. While the reason for building a cellular system in a hierarchical fashion has disappeared, there are other good reasons to make the system architecture flat: (1) as wireless transmission techniques evolve into hybrid ARQ systems, there is less need for a hierarchical cellular system to support spatial diversity; (2) we foresee that future cellular networks are part of the Internet, while hierarchical systems typically use interfaces between network elements that are specific to cellular standards or proprietary. At best such systems use IP as a transport medium, not as a core component; (3) a flat cellular system can be self scaling while a hierarchical system has inherent scaling issues; (4) moving all access technologies to the edge of the network enables ease of converging access technologies into a common packet core; and (5) using an IP common core makes the cellular network part of the Internet

Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws

We study a system of hard-core particles sliding downwards on a fluctuating one-dimensional surface which is characterized by a dynamical exponent $z$. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale $\sim t^{1/z}$. The structure factor deviates from the Porod law in some cases. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provides insight into the origin of this behaviour.Comment: 5 pages, 5 Postscript figure

Finite size scaling for the core of large random hypergraphs

The (two) core of a hypergraph is the maximal collection of hyperedges within which no vertex appears only once. It is of importance in tasks such as efficiently solving a large linear system over GF[2], or iterative decoding of low-density parity-check codes used over the binary erasure channel. Similar structures emerge in a variety of NP-hard combinatorial optimization and decision problems, from vertex cover to satisfiability. For a uniformly chosen random hypergraph of $m=n\rho$ vertices and $n$ hyperedges, each consisting of the same fixed number $l\geq3$ of vertices, the size of the core exhibits for large $n$ a first-order phase transition, changing from $o(n)$ for $\rho>\rho _{\mathrm{c}}$ to a positive fraction of $n$ for $\rho<\rho_{\mathrm{c}}$, with a transition window size $\Theta(n^{-1/2})$ around $\rho_{\mathrm{c}}>0$. Analyzing the corresponding ``leaf removal'' algorithm, we determine the associated finite-size scaling behavior. In particular, if $\rho$ is inside the scaling window (more precisely, $\rho=\rho_{\mathrm{c}}+rn^{-1/2}$), the probability of having a core of size $\Theta(n)$ has a limit strictly between 0 and 1, and a leading correction of order $\Theta(n^{-1/6})$. The correction admits a sharp characterization in terms of the distribution of a Brownian motion with quadratic shift, from which it inherits the scaling with $n$. This behavior is expected to be universal for a wide collection of combinatorial problems.Comment: Published in at http://dx.doi.org/10.1214/07-AAP514 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions

Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated by means of the exact-diagonalization method for the system sizes up to L=5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate, with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as nu=2.3(0.6) and z=2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical response function) is expressed in terms of the continued-fraction form consisted of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as sigma_c(omega=0)=0.135(0.01) ((2e)^2/h)