A Note on Power-Laws of Internet Topology

The three Power-Laws proposed by Faloutsos et al(1999) are important discoveries among many recent works on finding hidden rules in the seemingly chaotic Internet topology. In this note, we want to point out that the first two laws discovered by Faloutsos et al(1999, hereafter, {\it Faloutsos' Power Laws}) are in fact equivalent. That is, as long as any one of them is true, the other can be derived from it, and {\it vice versa}. Although these two laws are equivalent, they provide different ways to measure the exponents of their corresponding power law relations. We also show that these two measures will give equivalent results, but with different error bars. We argue that for nodes of not very large out-degree($\leq 32$ in our simulation), the first Faloutsos' Power Law is superior to the second one in giving a better estimate of the exponent, while for nodes of very large out-degree($> 32$) the power law relation may not be present, at least for the relation between the frequency of out-degree and node out-degree.Comment: 16 pages, 3 figure

Kinetics and thermodynamics across single-file pores: solute permeability and rectified osmosis

We study the effects of solute interactions on osmotic transport through pores. By extending single-file, single-species kinetic models to include entrance of solute into membrane pores, we model the statistical mechanics of competitive transport of two species across membrane pores. The results have direct applications to water transport across biomembrane pores and particle movement in zeolites, and can be extended to study ion channel transport. Reflection coefficients, the reduction of osmotic fluxes measured using different solutes, are computed in terms of the microscopic kinetic parameters. We find that a reduction in solvent flow due to solute-pore interactions can be modelled by a Langmuir adsorption isotherm. Osmosis experiments are discussed and proposed. Special cases and Onsager relations are presented in the Appendices.Comment: 15pp, 9 .eps figures. Accepted to J. Chem. Phys. 199

Rapid Cycling Synchrotron Option for Project X

This paper presents an 8 GeV Rapid Cycling Synchrotron (RCS) option for Project X. It has several advantages over an 8 GeV SC linac. In particular, the cost could be lower. With a 2 GeV 10 mA pulsed linac as injector, the RCS would be able to deliver 4 MW beam power for a muon collider. If, instead, a 2 GeV 1 mA CW linac is used, the RCS would still be able to meet the Project X requirements but it would be difficult for it to serve a muon collider due to the very long injection time.Comment: 4 pages, 2 figures, presentation at the Workshop on Applications of High Intensity Proton Accelerators AHIPA0