The bounds of heavy-tailed return distributions in evolving complex networks

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows the emergence of critical behavior. Starting from a brief discussion about the main features of the evolving network of trades, we show that the logarithmic return distributions have bounded heavy tails, and the corresponding bounding exponent values can be derived. Finally, we discuss these findings in the context of model risk.     

Flow field studies on a micro-air-vehicle-scale cycloidal rotor in forward flight

This paper examines the flow physics and principles of force production on a cycloidal rotor (cyclorotor) in forward flight. The cyclorotor considered here consists of two blades rotating about a horizontal axis, with cyclic pitch angle variation about the blade quarter-chord. The flow field at the rotor mid-span is analyzed using smoke flow visualization and particle image velocimeV are compared with flow fields predicted using 2D CFD and time-averaged force measurements acquired in an open-jet wind tunnel at three advance ratios. It is shown that the experimental flow field is nearly two dimensional at μ = 0.73 allowing for qualitative comparisons to be made with CFD. The incoming flow velocity decreases in magnitude as the flow passes through the retreating (upper) half of the rotor and is attributed to power extraction by the blades. A significant increase in flow velocity is observed across the advancing (lower) half of the rotor. The aerodynamic analysis demonstrates that the blades accelerate the flow through the lower aft region of the rotor, where they operate in a high dynamic pressure environment. This is consistent with CFD-predicted values of instantaneous aerodynamic forces which reveal that the aft section of the rotor is the primary region of force production. Phase-averaged flow field measurements showed two blade wakes in the flow, formed by each of the two blades. Analysis of the blades at several azimuthal positions revealed two significant blade-wake interactions. The locations of these blade-wake interactions are correlated with force peaks in the CFD-predicted instantaneous blade forces and highlight their importance to the generation of lift and propulsive force of the cyclorotor.     

Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves

The incompressible smoothed particle hydrodynamics (ISPH) method with projection-based pressure correction has been shown to be highly accurate and stable for internal flows and, importantly for many problems, the pressure field is virtually noise-free in contrast to the weakly compressible SPH approach (Xu et al., 2009 [31]). However for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels. A new algorithm is presented which remedies this issue, giving stable and accurate solutions to both internal and free-surface flows. Generalising the particle shifting approach of Xu et al. (2009) [31], the algorithm is based upon Fick’s law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability. The algorithm is validated against analytical solutions for an internal flow at higher Reynolds numbers than previously, the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times. The method is then validated for progressive regular waves with paddle motion defined by linear theory. The accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels. The test cases are thought to provide a more thorough quantitative validation than previously undertaken.     

On moduli of p-continuity

Moduli of p-continuity provide a measure of fractional smoothness of functions via p-variation. We prove a sharp estimate of the modulus of p-continuity in terms of the modulus of q-continuity (1<p<q<??).     

Gamma-gamma energy correlations and moment of inertia in light Xe isotopes

High-spin properties of even ^118–122Xe isotopes have been studied in experiments when a 118 MeV ¹²C beam impinged on ¹¹⁴Cd and ¹¹⁶Cd targets. The γ-rays emitted following the reactions were detected by six NaI(Tl) counters. The coincidence events from the counters were sorted into a two-dimensional matrices, from which the energy-correlation spectra were extracted. From the energy correlation spectra the quantities of the collective moment of inertia $\text{I}$⁽²⁾ are deduced and compared with data obtained for the same nuclei in previous experiments, as well as with results from theoretical studies.     

Ergodic group automorphisms are exponentially recurrent

We show that ergodic automorphisms of compact abelian groups have the property that for every nonempty open setU, the measure of the set first returning toU aftern iterates decays exponentially inn. This follows from a result about aperiodic automorphisms of countable abelian groups, whose proof employsp-adic analysis. Partially supported by NSF Grant MCS 7704915.     

Quality control samples for the determination of lead and cadmium in blood, feces, air filters, and dust

Summary Quality control samples for the determination of lead and cadmium in blood, feces, air filters, and dust have been prepared within the UNEP/WHO Human Exposure Assessment Location (HEAL) Project. The preparation is given in detail. Problems related to sample preparation and reference values are discussed.

---

Qualitätskontrollproben für die Bestimmung von Blei und Cadmium in Blut, Faeces, Luftfiltern und Staub

     

Zirconium tungstate hydroxide hydrate revisited: Crystallization dependence on halide and hydronium ions

The formation of zirconium tungstate hydroxide hydrate, a precursor to the negative thermal expansion material cubic zirconium tungstate, shows a strong dependence on hydrothermal reaction conditions. It was found that not only the acid concentration, but also the acid counterion plays a significant role in the crystallization of ZrW₂O₇(OH)₂·2H₂O. High temperatures, high acid concentrations, and the presence of chloride or bromide ions promote the formation of well-crystallized ZrW₂O₇(OH)₂·2H₂O. For low acid concentrations, a new zirconium tungstate hydrate polymorph is observed, which transforms to tetragonal ZrW₂O₇(OH)₂·2H₂O at longer reaction times. A study of crystallization kinetics in hydrochloric acid is presented.