Nonlinear Particle Acceleration in Relativistic Shocks

Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to increase above test-particle values. Modified shocks with Lorentz factors less than about 3 can have compression ratios considerably greater than 3 and the momentum distribution of energetic particles no longer follows a power law relation. These results may be important for the interpretation of gamma-ray bursts if mildly relativistic internal and/or afterglow shocks play an important role accelerating particles that produce the observed radiation. For shock Lorentz factors greater than about 10, r approaches 3 and the so-called `universal' test-particle result of N(E) proportional to E^{-2.3} is obtained for sufficiently energetic particles. In all cases, the absolute normalization of the particle distribution follows directly from our model assumptions and is explicitly determined.Comment: Updated version, Astroparticle Physics, in press, 29 pages, 13 figure

Artificial broadening of the high-energy end of electron spectrum in supernova remnants

The observed spectrum of a supernova remnant (SNR) is a superposition of many ``local'' spectra emitted by regions of SNRs that are under different physical conditions. The question remains as to whether the broadening of the high-energy end of the observed nonthermal spectrum of SNRs, like in G347.3-0.5 and SN 1006, can be an artifact of observations or it is a consequence of the microphysics involved in the acceleration process. In this note we study the influence of parameters variations (inside the volume and over the surface of SNR) on the shape of the high-energy end of the synchrotron (and also inverse Compton) spectrum. We consider three possibilities for these parameter variations: i) gradients downstream of the shock with constant maximum energy of the accelerated electrons and the potential variation in time of the injection efficiency, ii) then we add the possibility of the maximum energy depending on time, and finally iii) the possible obliquity dependences of maximum energy and injection efficiency. It is shown that gradients of density and magnetic field strength downstream of the shock are ineffective in modifying the shape of the synchrotron spectrum, even if an SNR evolves in the nonuniform interstellar medium and/or the injection efficiency varies in time. The time dependence of the maximum energy of the electrons accelerated by the shock is also not able to make the observed spectrum much broader. The only possibility of producing considerable broadening in the spectrum is the variation in the maximum energy of electrons over the surface of SNR. In such a case, the obliquity dependence of the injection efficiency also affects the shape of the spectrum, but its role is less significant.Comment: 6 pages, 4 figures, A&A accepte

A Novel Approach to Non linear Shock Acceleration

First order Fermi acceleration at astrophysical shocks is often invoked as a mechanism for the generation of non-thermal particles. This mechanism is especially simple in the approximation that the accelerated particles behave like test particles, not affecting the shocked fluid. Many complications enter the calculations when the accelerated particles have a backreaction on the fluid, in which case we may enter the non linear regime of shock acceleration. In this paper we summarize the main features of a semi-analytical approach to the study of the non linearity in shock acceleration, and compare some of the results with previous attempts and with the output of numerical simulations.Comment: To appear in the proceedings of the TAUP conference, September 8-12, 2001 - Gran Sasso Laboratory, Ital

A semi-analytical approach to non-linear shock acceleration

Shocks in astrophysical fluids can generate suprathermal particles by first order (or diffusive) Fermi acceleration. In the test particle regime there is a simple relation between the spectrum of the accelerated particles and the jump conditions at the shock. This simple picture becomes complicated when the pressure of the accelerated particles becomes comparable with the pressure of the shocked fluid, so that the non-linear backreaction of the particles becomes non negligible and the spectrum is affected in a substantial way. Though only numerical simulations can provide a fully self-consistent approach, a more direct and easily applicable method would be very useful, and would allow to take into account the non-linear effects in particle acceleration in those cases in which they are important and still neglected. We present here a simple semi-analytical model that deals with these non-linear effects in a quantitative way. This new method, while compatible with the previous simplified results, also provides a satisfactory description of the results of numerical simulations of shock acceleration.Comment: 20 pages, 9 figures. To appear in Astroparticle Physic

Strategic Entry Deterrence and the Behavior of Pharmaceutical Incumbents Prior to Patent Expiration

This paper develops a new approach to testing for strategic entry deterrence and applies it to the behavior of pharmaceutical incumbents just before they lose patent protection. The approach involves looking at a cross-section of markets and examining whether behavior is nonmonotonic in the size of the market. Under certain conditions, investment levels will be monotone in market size if firms are not influenced by a desire to deter entry. Strategic investments, however, may be nonmonotone because entry deterrence is unnecessary in very small markets and impossible in very large ones, resulting in overall nonmonotonic investment. The pharmaceutical data contain advertising, product proliferation, and pricing information for a sample of drugs which lost patent protection between 1986 and 1992. Among the findings consistent with an entry deterrence motivation are that incumbents in markets of intermediate size have lower levels of advertising and are more likely to reduce advertising immediately prior to patent expiration.

Weighting the politics of the environment in the new Europe

EU membership imposes significant environmental pressures on the New Member states (NMS’s). This paper questions whether top down imposition of EU environmental regulation is the best strategy for the environmental problems of Central and Eastern Europe. While the emissions ’ record has greatly improved, it remains un-clear how much of this is directly related to EU membership. Sig-nificant costs are attached to fulfilling EU environmental criteria while remarkably smaller amounts of funding come attached to the EU membership agreement. Top-down imposition of environmental objectives may divert attention from local, regional and state level environmental needs, preferences and priorities. Accepting the man-tle of EU environmental policy means adopting a policy structure that, in many ways, is dominated by the interests and priorities of the large and more advanced EU Member states. The findings of this paper have significant implications for the lobbying activities of the NMS’s, for the weighting of the pollution burden in the New Europe and for future constitutional debates

Market correctives, market palliatives and the new politics of European industrial and regional development

This paper argues that the New Economy paradigm and the interests of the more advanced EU Member states dominate current thinking on EU industrial and regional policy. European integration is driving a political economy of regionalism that—far more than traditional divisions between labour and capital—decisively defines the contours of “economic interests” in the New Europe and has the most significant impact on EU, national and subnational policy approaches. The New Economy paradigm is driving a radical shift in EU policy from cohesion or redistribution toward innova-tion promotion and affects distributional struggles at the EU, national and subnational levels. This shift has important implications for future EU in-dustrial and regional development policy goals. On the one hand, shifting strategies pose significant challenges at the national and subnational levels. While political decentralization dominates current discourse, national gov-ernments—in particular perhaps in the New Member states (NMS’s)—are more likely to favour centralized control over national and regional spend-ing priorities. On the other hand, seemingly at the expense of the NMS’s, the increasing concentration of EU funding on a large number of less ad-vanced economies is eroding the policy’s traditional support basis

W and Z Properties at the Tevatron

We present recent results from CDF and D0 on W and Z production cross sections, the width of the W boson, tau-e universality in W decays, trilinear gauge boson couplings, and on the observation of Z -> b bbar.Comment: Paper presented at the International Europhysics Conference on High Energy Physics, Tampere, Finland, 15-21 July, 199

Internet Retail Demand: Taxes, Geography, and Online-Offline Competition

Data on sales of memory modules are used to explore several aspects of e-retail demand. There is a strong relationship between e-retail sales to a given state and sales tax rates that apply to purchases from online retailers. This suggests that there is substantial substitution between online and online retail, and tax avoidance may be an important contributor to e-retail activity. Geography matters in two ways: we find some evidence that consumers prefer purchasing from firms in nearby states to benefit from faster shipping times as well as evidence of a separate preference for buying from in-state firms. Consumers appear fairly rational in some ways, but boundedly rational in others.