11,542 research outputs found
Non-linear diffusive shock acceleration with free escape boundary
We present here a semi-analytical solution of the problem of particle
acceleration at non-linear shock waves with a free escape boundary at some
location upstream. This solution, besides allowing us to determine the spectrum
of particles accelerated at the shock front, including the shape of the cutoff
at some maximum momentum, also allows us to determine the spectrum of particles
escaping the system from upstream. This latter aspect of the problem is crucial
for establishing a connection between the accelerated particles in
astrophysical sources, such as supernova remnants, and the cosmic rays observed
at the Earth. An excellent approximate solution, which leads to a
computationally fast calculation of the structure of shocks with an arbitrary
level of cosmic ray modification, is also obtained.Comment: 11 pages, 2 figures, Accepted for publication in APh
The role of forecasts in monetary policy
Forecasts of future economic developments play an important role for the monetary policy decisions of central banks. For example, forecasts of goal variables can help central banks achieve their goals and make them more accountable to the public. There are two primary explanations for the benefits of forecasts. The first is that monetary policy affects goal variables such as inflation and output only with substantial lags. Policy actions should, therefore, be based on forecasts of goal variables at horizons consistent with policy lags and be taken when these forecasts are inconsistent with policy goals. Under such an approach, the quality of a central bank's forecasts and the effectiveness of its actions to bring forecasts into alignment with targets provide a basis for judging the performance of policymakers and for holding them accountable.> The second, and less intuitive, explanation is that by focusing on a forecast of only one variable -- inflation -- a central bank can potentially achieve multiple goals. This approach can be successful even if there are tradeoffs among the various goal variables. For example, the approach can combine a commitment to long-run price stability with concern for the effects of monetary policy on output.> Amato and Laubach argue that the lagged effects of monetary policy make the use of forecasts necessary. They also argue that delegating a single goal—such as inflation stabilization—to the central bank facilitates accountability, but at the risk of not achieving other goals. They then examine how the Eurosystem and the Bank of England, both of which have been assigned a single goal, address the existence of tradeoffs among goals. Finally, the authors provide evidence that a monetary policy aimed primarily at stabilizing inflation forecasts—as practiced by the Bank of England, for example—can, in fact, achieve multiple goals.Forecasting ; Monetary policy ; Banks and banking, Central
The value of interest rate smoothing : how the private sector helps the Federal Reserve
Most central banks conduct monetary policy by setting targets for overnight interest rates. During the 1990s, central banks have tended to move these interest rates in small steps without reversing direction quickly, a practice called interest rate smoothing. For example, the majority of Federal Reserve policy moves in the last decade and a half have come in a sequence of 25 basis point moves, in striking contrast to the early 1980s, when short-term interest rates fluctuated widely. In light of this historical contrast, it is natural to ask whether interest rate smoothing is a desirable way to conduct monetary policy.> Amato and Laubach argue that interest rate smoothing is beneficial because the private sector is forward-looking. The private sector bases its decisions on expectations of the future. Thus, a monetary policy move today will be more effective if it is expected to persist over time. By smoothing interest rates, the size of changes in interest rates required to reduce fluctuations in the economy can be smaller than would otherwise be necessary.Monetary policy ; Interest rates ; Monetary policy - United States
On the escape of particles from cosmic ray modified shocks
Stationary solutions to the problem of particle acceleration at shock waves
in the non-linear regime, when the dynamical reaction of the accelerated
particles on the shock cannot be neglected, are known to show a prominent
energy flux escaping from the shock towards upstream infinity. On physical
grounds, the escape of particles from the upstream region of a shock has to be
expected in all those situations in which the maximum momentum of accelerated
particles, , decreases with time, as is the case for the Sedov-Taylor
phase of expansion of a shell Supernova Remnant, when both the shock velocity
and the cosmic ray induced magnetization decrease. In this situation, at each
time , particles with momenta larger than leave the system from
upstream, carrying away a large fraction of the energy if the shock is strongly
modified by the presence of cosmic rays. This phenomenon is of crucial
importance for explaining the cosmic ray spectrum detected at Earth. In this
paper we discuss how this escape flux appears in the different approaches to
non-linear diffusive shock acceleration, and especially in the quasi-stationary
semi-analytical kinetic ones. We apply our calculations to the Sedov-Taylor
phase of a typical supernova remnant, including in a self-consistent way
particle acceleration, magnetic field amplification and the dynamical reaction
on the shock structure of both particles and fields. Within this framework we
calculate the temporal evolution of the maximum energy reached by the
accelerated particles and of the escape flux towards upstream infinity. The
latter quantity is directly related to the cosmic ray spectrum detected at
Earth.Comment: Version accepted for publication in MNRA
Dynamical effects of self-generated magnetic fields in cosmic ray modified shocks
Recent observations of greatly amplified magnetic fields () around supernova shocks are consistent with the predictions of the
non-linear theory of particle acceleration (NLT), if the field is generated
upstream of the shock by cosmic ray induced streaming instability. The high
acceleration efficiencies and large shock modifications predicted by NLT need
however to be mitigated to confront observations, and this is usually assumed
to be accomplished by some form of turbulent heating. We show here that
magnetic fields with the strength inferred from observations have an important
dynamical role on the shock, and imply a shock modification substantially
reduced with respect to the naive unmagnetized case. The effect appears as soon
as the pressure in the turbulent magnetic field becomes comparable with the
pressure of the thermal gas. The relative importance of this unavoidable effect
and of the poorly known turbulent heating is assessed. More specifically we
conclude that even in the cases in which turbulent heating may be of some
importance, the dynamical reaction of the field cannot be neglected, as instead
is usually done in most current calculations.Comment: 4 pages, 1 figure, accepted for publication in ApJ Letter
The contribution of supernova remnants to the galactic cosmic ray spectrum
The supernova paradigm for the origin of galactic cosmic rays has been deeply
affected by the development of the non-linear theory of particle acceleration
at shock waves. Here we discuss the implications of applying such theory to the
calculation of the spectrum of cosmic rays at Earth as accelerated in supernova
remnants and propagating in the Galaxy. The spectrum is calculated taking into
account the dynamical reaction of the accelerated particles on the shock, the
generation of magnetic turbulence which enhances the scattering near the shock,
and the dynamical reaction of the amplified field on the plasma. Most
important, the spectrum of cosmic rays at Earth is calculated taking into
account the flux of particles escaping from upstream during the Sedov-Taylor
phase and the adiabatically decompressed particles confined in the expanding
shell and escaping at later times. We show how the spectrum obtained in this
way is well described by a power law in momentum with spectral index close to
-4, despite the concave shape of the instantaneous spectra of accelerated
particles. On the other hand we also show how the shape of the spectrum is
sensible to details of the acceleration process and environment which are and
will probably remain very poorly known.Comment: 19 pages, 8 figures, published version (references updated
Modelling aspects of the inflation process and the monetary transmission mechanism in emerging market countries
Frequency domain analysis of the mean and osculating trajectories of LAGEOS-1
Several crucial developments in orbital mechanics are obtained through the method of averaging, which is equivalent to integrating only the dominant harmonics of the Fourier series of the dynamics. Frequency analysis of the trajectory expressed in orbital elements facilitates an in-depth understanding of Earth satellite dynamics, and facilitates the interpretation of numerical results from special perturbations within the theoretical framework of celestial mechanics. In this work, we examine recent Two-Line Element series for LAGEOS-1 in the frequency domain, highlighting the presence of short-periodic terms that are likely introduced in the generation of TLEs from observations. We also propose employing well-established methods from signal processing, such as spectrograms, to examine the evolution of dissipative systems such as satellites in LEO
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