A strictly Markovian expansion for plasma turbulence theory

The collision operator that appears in the equation of motion for a particle distribution function that was averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. An expansion is derived for the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasilinear expansion

A dynamic equation for stochastic magnetic field lines in the galaxy

Dynamic equations for stochastic magnetic field lines in galax

An autocorrelation approach to the Brown Twiss interferometer

Autocorrelation of incoherent stellar light measured by interferomete

International Trade: Rules of Origin

[Excerpt] Determining the country of origin of a product is important for properly assessing tariffs, enforcing trade remedies (such as anti-dumping and countervailing duties) or quantitative restrictions (tariff quotas), and statistical purposes. Other commercial trade policies are also linked with origin determinations, such as country of origin labeling and government procurement regulations. Rules of origin (ROO), used to determine the country of origin of merchandise entering the U.S. market, can be very simple, noncontroversial tools of international trade as long as all of the parts of a product are manufactured and assembled primarily in one country. However, when a finished product’s component parts originate in many countries, as is often the case in today’s global trading environment, determining origin can be a very complex, sometimes subjective, and time-consuming process. U.S. Customs and Border Protection (CBP) is the agency responsible for determining country of origin using various ROO schemes. Non-preferential rules of origin are used to determine the origin of goods imported from countries with which the United States has most-favored-nation (MFN) status. They are the principal regulatory tools for accurate assessment of tariffs on imports, addressing country of origin labeling issues, qualifying goods for government procurement, and enforcing trade remedy actions and trade sanctions. Preferential rules are used to determine the eligibility of imported goods from certain U.S. free trade agreement (FTA) partners and certain developing country beneficiaries to receive duty-free or reduced tariff benefits under bilateral or regional FTAs, trade preference programs (such as the Generalized System of Preferences), and other special import programs. Preferential rules of origin are specific to each FTA, which means that they vary from agreement to agreement and preference to preference. This report deals with ROO in three parts. First, we describe in more detail the reasons that country of origin rules are important and briefly describe U.S. laws and methods that provide direction in making these determinations. Second, we discuss briefly some of the more controversial issues involving rules of origin, including the apparently subjective nature of some CBP origin determinations, and the effects of the global manufacturing process on ROO. Third, we conclude with some alternatives and options that Congress could consider that might assist in simplifying the process. This report will be updated as events warrant

The galactic halo question: New size constraints from galactic gamma-ray data

The SAS-2 gamma-ray data is analyzed making use of recent CO line emission and other data for determining the large-scale distribution of galactic gas. A nonuniform distribution of cosmic rays in the galaxy is implied. This fact rules out large trapping halo models and extragalactic origin models. Detailed models of diffusion halos of various sizes perpendicular to the galactic plane are considered. In such models, the scale perpendicular to the plane has a strong effect in determining the radial distribution of cosmic rays. Such radial distributions are calculated for cylindrical coordinate models. The implied gamma-ray longitude distributions are then calculated and compared with the SAS-2 data for goodness-of-fit. Assuming the sources to be supernova remnants or pulsars, cosmic ray nucleon halo models with scale heights greater than 3 kpc are found to provide a poor fit to the gamma-ray longitude data (probability of 6% or less). Thin halo, or source dominated diffusion models are found to provide a good fit to the gamma-ray data, with an upper limit scale height of approximately 3 kpc

International Trade: Rules of Origin

[Excerpt] Recent trade policy issues have pointed to the framework used by the United States and other countries to regulate imports, including the process of determining country of origin using “rules of origin” (ROO). Such rules can be very simple, noncontroversial tools of international trade as long as all of the parts of a product are manufactured and assembled primarily in one country. However, when a finished product’s component parts originate in many countries—as is often the case in today’s global trading environment—determining origin can be a very complex, sometimes subjective, and time-consuming process. This report first provides a general overview of the U.S. ROO system, including its implementation as it applies to manufactured imports. Second, advantages and disadvantages of the ROO schemes as implemented by the United States are also discussed. Third, the report illustrates ways in which the application of the rules of origin system can lead to country of origin determinations that could be inconsistent with U.S. policy objectives or goals, or encourage businesses to circumvent them. The report concludes with some options that Congress could consider in order to improve the ROO process

Acceleration Rates and Injection Efficiencies in Oblique Shocks

The rate at which particles are accelerated by the first-order Fermi mechanism in shocks depends on the angle, \teq{\Tbone}, that the upstream magnetic field makes with the shock normal. The greater the obliquity the greater the rate, and in quasi-perpendicular shocks rates can be hundreds of times higher than those seen in parallel shocks. In many circumstances pertaining to evolving shocks (\eg, supernova blast waves and interplanetary traveling shocks), high acceleration rates imply high maximum particle energies and obliquity effects may have important astrophysical consequences. However, as is demonstrated here, the efficiency for injecting thermal particles into the acceleration mechanism also depends strongly on obliquity and, in general, varies inversely with \teq{\Tbone}. The degree of turbulence and the resulting cross-field diffusion strongly influences both injection efficiency and acceleration rates. The test particle \mc simulation of shock acceleration used here assumes large-angle scattering, computes particle orbits exactly in shocked, laminar, non-relativistic flows, and calculates the injection efficiency as a function of obliquity, Mach number, and degree of turbulence. We find that turbulence must be quite strong for high Mach number, highly oblique shocks to inject significant numbers of thermal particles and that only modest gains in acceleration rates can be expected for strong oblique shocks over parallel ones if the only source of seed particles is the thermal background.Comment: 24 pages including 6 encapsulated figures, as a compressed, uuencoded, Postscript file. Accepted for publication in the Astrophysical Journa

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory