37 research outputs found
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
Microflares and the Statistics of X-ray Flares
This review surveys the statistics of solar X-ray flares, emphasising the new
views that RHESSI has given us of the weaker events (the microflares). The new
data reveal that these microflares strongly resemble more energetic events in
most respects; they occur solely within active regions and exhibit
high-temperature/nonthermal emissions in approximately the same proportion as
major events. We discuss the distributions of flare parameters (e.g., peak
flux) and how these parameters correlate, for instance via the Neupert effect.
We also highlight the systematic biases involved in intercomparing data
representing many decades of event magnitude. The intermittency of the
flare/microflare occurrence, both in space and in time, argues that these
discrete events do not explain general coronal heating, either in active
regions or in the quiet Sun.Comment: To be published in Space Science Reviews (2011
An Observational Overview of Solar Flares
We present an overview of solar flares and associated phenomena, drawing upon
a wide range of observational data primarily from the RHESSI era. Following an
introductory discussion and overview of the status of observational
capabilities, the article is split into topical sections which deal with
different areas of flare phenomena (footpoints and ribbons, coronal sources,
relationship to coronal mass ejections) and their interconnections. We also
discuss flare soft X-ray spectroscopy and the energetics of the process. The
emphasis is to describe the observations from multiple points of view, while
bearing in mind the models that link them to each other and to theory. The
present theoretical and observational understanding of solar flares is far from
complete, so we conclude with a brief discussion of models, and a list of
missing but important observations.Comment: This is an article for a monograph on the physics of solar flares,
inspired by RHESSI observations. The individual articles are to appear in
Space Science Reviews (2011