Scattering of a Plane Acoustical Wave by a Spherical Obstacle

The long-time behavior of the scattered field produced by a plane acoustical pulse stalking a spherical obstacle is investigated. Incident pulses are taken that represent a unit step in potential (or equivalently delta function pulse in pressure), an arbitrary potential pulse of finite duration, and an arbitrary pressure pulse of finite duration. Both hard and soft spheres are considered. In addition, a pulse consisting of a unit step in velocity impinging on a hard sphere is examined. In each case, the time rate of decay to the steady state is established. This is seen to be controlled by the zeroes of certain naturally occurring special polynomials that arise because of the spherical geometry and are independent of the shape of the incident pulse

To Aggregate, Pool, or Neither: Testing the Rational Expectations Hypothesis Using Survey Data

It is well known that even if all forecasters are rational, estimated coefficients in unbiasedness regressions using consensus forecasts are inconsistent because forecasters have private information. However, if all forecasters face a common realization, pooled estimators are also inconsistent. In contrast, we show that when predictions and realizations are integrated and cointegrated, micro-homogeneity ensures that consensus and pooled estimators are consistent. Therefore, contrary to claims in the literature, in the absence of micro-homogeneity, pooling is not a solution to the aggregation problem. We reject micro-homogeneity for a number of forecasts from the Survey of Professional Forecasters. Therefore, for these variables unbiasedness can only be tested at the individual level.Rational Expectations, Micro-homogeneity, Heterogeneity Bias, Aggregation Bias, Survey Forecasts

Testing the Rational Expectations Hypothesis using Survey Data

Because of the importance of inflation expectations, Lloyd B. Thomas Jr. (Fall 1999, p. 125-44) reexamines "the evidence on the nature and performance of various measures of expected inflation, with special attention given to the issue of rationality" (p. 126). Thomas tests the unbiasedness hypothesis using the Livingston and Michigan survey forecasts for the 1960 to 1997 time period and is unable to reject the null hypothesis of unbiasedness. Unfortunately, two types of problems due to aggregation plague such tests: private information bias and micro-heterogeneity bias. Therefore, for these survey forecasts, consensus regressions should generally not be used to test rationality; rationality can only be tested at the individual level.

Quantifying nonorthogonality

An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to single-particle density matrices using methods that are similar to recently introduced techniques for quantifying entanglement. Several interesting special cases are considered. It is pointed out that a measure of nonorthogonality can meaningfully be associated with a single mixed quantum state. It is then shown how nonorthogonality can be unlocked with classical information; this analysis reveals interesting inequalities and points to a number of connections between nonorthogonality and entanglement.Comment: Accepted for publication in Phys. Rev.

Sheath ionization model of beam emissions from large spacecraft

An analytical model of the charging of a spacecraft emitting electron and ion beams has been applied to the case of large spacecraft. In this model, ionization occurs in the sheath due to the return current. Charge neutralization of spherical space charge flow is examined by solving analytical equations numerically. Parametric studies of potential large spacecraft are performed. As in the case of small spacecraft, the ions created in the sheath by the returning current play a large role in determining spacecraft potential

Optimization of Network Robustness to Waves of Targeted and Random Attack

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions $p_t$ and $p_r$ respectively of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction $r$ of the nodes having degree k_2= (\kav - 1 +r)/r and the remainder of the nodes having degree $k_1=1$, where \kav is the average degree of all the nodes. We find that the optimal value of $r$ is of the order of $p_t/p_r$ for $p_t/p_r\ll 1$

Modeling the Internet's Large-Scale Topology

Network generators that capture the Internet's large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internet's evolution. By combining the most extensive data on the time evolution, topology and physical layout of the Internet, we identify the universal mechanisms that shape the Internet's router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently employed exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models, and indicate that the networks created by all available topology generators are significantly different from the Internet

Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions

We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv a \bmod{q}} (\log(1-1/p)+1/p)$, for $q \in \{3$, ..., $100\}$ and $(q, a) = 1$.Comment: 12 pages, 6 table

X-Ray Emission-Line Profile Modeling Of O Stars: Fitting A Spherically Symmetric Analytic Wind-Shock Model To The Chandra Spectrum Of Zeta Puppis

X-ray emission-line profiles provide the most direct insight into the dynamics and spatial distribution of the hot, X-ray-emitting plasma above the surfaces of OB stars. The O supergiant zeta Puppis shows broad, blueshifted, and asymmetric line profiles, generally consistent with the wind-shock picture of OB star X-ray production. We model the profiles of eight lines in the Chandra HETGS spectrum of this prototypical hot star. The fitted lines indicate that the plasma is distributed throughout the wind starting close to the photosphere, that there is significantly less attenuation of the X-rays by the overlying wind than is generally supposed, and that there is not a strong trend in wind absorption with wavelength