63,537 research outputs found
The spectral difference between solar flare HXR coronal and footpoint sources due to wave-particle interactions
Investigate the spatial and spectral evolution of hard X-ray (HXR) emission
from flare accelerated electron beams subject to collisional transport and
wave-particle interactions in the solar atmosphere. We numerically follow the
propagation of a power-law of accelerated electrons in 1D space and time with
the response of the background plasma in the form of Langmuir waves using the
quasilinear approximation.}{We find that the addition of wave-particle
interactions to collisional transport for a transient initially injected
electron beam flattens the spectrum of the footpoint source. The coronal source
is unchanged and so the difference in the spectral indices between the coronal
and footpoint sources is \Delta \gamma > 2, which is larger than expected from
purely collisional transport. A steady-state beam shows little difference
between the two cases, as has been previously found, as a transiently injected
electron beam is required to produce significant wave growth, especially at
higher velocities. With this transiently injected beam the wave-particle
interactions dominate in the corona whereas the collisional losses dominate in
the chromosphere. The shape of the spectrum is different with increasing
electron beam density in the wave-particle interaction case whereas with purely
collisional transport only the normalisation is changed. We also find that the
starting height of the source electron beam above the photosphere affects the
spectral index of the footpoint when Langmuir wave growth is included. This may
account for the differing spectral indices found between double footpoints if
asymmetrical injection has occurred in the flaring loop.Comment: 10 pages, 10 FIgures, accepted for publication in A&
Broken phase effective potential in the two-loop Phi-derivable approximation and nature of the phase transition in a scalar theory
We study the phase transition of a real scalar phi^4 theory in the two-loop
Phi-derivable approximation using the imaginary time formalism, extending our
previous (analytical) discussion of the Hartree approximation. We combine Fast
Fourier Transform algorithms and accelerated Matsubara sums in order to achieve
a high accuracy. Our results confirm and complete earlier ones obtained in the
real time formalism [1] but which were less accurate due to the integration in
Minkowski space and the discretization of the spectral density function. We
also provide a complete and explicit discussion of the renormalization of the
two-loop Phi-derivable approximation at finite temperature, both in the
symmetric and in the broken phase, which was already used in the real-time
approach, but never published. Our main result is that the two-loop
Phi-derivable approximation suffices to cure the problem of the Hartree
approximation regarding the order of the transition: the transition is of the
second order type, as expected on general grounds. The corresponding critical
exponents are, however, of the mean-field type. Using a "RG-improved" version
of the approximation, motivated by our renormalization procedure, we find that
the exponents are modified. In particular, the exponent delta, which relates
the field expectation value phi to an external field h, changes from 3 to 5,
getting then closer to its expected value 4.789, obtained from accurate
numerical estimates [2].Comment: 54 pages, 16 figure
Accelerated Inexact Composite Gradient Methods for Nonconvex Spectral Optimization Problems
This paper presents two inexact composite gradient methods, one inner
accelerated and another doubly accelerated, for solving a class of nonconvex
spectral composite optimization problems. More specifically, the objective
function for these problems is of the form where and
are differentiable nonconvex matrix functions with Lipschitz continuous
gradients, is a proper closed convex matrix function, and both and
can be expressed as functions that operate on the singular values of their
inputs. The methods essentially use an accelerated composite gradient method to
solve a sequence of proximal subproblems involving the linear approximation of
and the singular value functions underlying and . Unlike other
composite gradient-based methods, the proposed methods take advantage of both
the composite and spectral structure underlying the objective function in order
to efficiently generate their solutions. Numerical experiments are presented to
demonstrate the practicality of these methods on a set of real-world and
randomly generated spectral optimization problems
Reconstruction of Inflation Models
In this paper, we reconstruct viable inflationary models by starting from
spectral index and tensor-to-scalar ratio from Planck observations. We analyze
three different kinds of models: scalar field theories, fluid cosmology and
f(R)-modified gravity. We recover the well known R^2-inflation in Jodan frame
and Einstein frame representation, the massive scalar inflaton models and two
models of inhomogeneous fluid. A model of R^2-correction to Einstein's gravity
plus a "cosmological constant" with an exact solution for early time
acceleration is reconstructed.Comment: 14 page
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