We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of hyperscaling due
to a dangerous irrelevant variable, applies only to k=0 fluctuations, and so there is only a single exponent eta describing power-law decay of correlations at criticality, in contrast to recent claims. With free boundary conditions the finite-size shift is greater than the rounding. Nonetheless, using T-T_L, where T_L is the finite-size pseudocritical temperature, rather than T-T_c, as the scaling variable, the data does collapse on to a scaling form which includes the behavior both at T_L, where the susceptibility chi diverges like L^{d/2} and at the bulk T_c where it diverges like L^2. These claims are supported by large-scale simulations on the 5-dimensional Ising model.
The Interface Region Imaging Spectrometer (IRIS) is the first solar instrument to observe $sim 10$ MK plasma at subarcsecond spatial resolution through imaging spectroscopy of the Fe XXI $lambda$1354.1 forbidden line. IRIS observations of the X1 clas
s flare that occurred on 2014 March 29 at 17:48 UT reveal Fe XXI emission from both the flare ribbons and the post-flare loop arcade. Fe XXI appears at all of the chromospheric ribbon sites, although typically with a delay of one raster (75 seconds) and sometimes offset by up to 1$^{primeprime}$. 100--200 km s$^{-1}$ blue-shifts are found at the brightest ribbons, suggesting hot plasma upflow into the corona. The Fe XXI ribbon emission is compact with a spatial extent of $< 2^{primeprime}$, and can extend beyond the chromospheric ribbon locations. Examples are found of both decreasing and increasing blue-shift in the direction away from the ribbon locations, and blue-shifts were present for at least 6 minutes after the flare peak. The post-flare loop arcade, seen in Atmospheric Imaging Assembly (AIA) 131 AA filtergram images that are dominated by Fe XXI, exhibited bright loop-tops with an asymmetric intensity distribution. The sizes of the loop-tops are resolved by IRIS at $ge 1^{primeprime}$, and line widths in the loop-tops are not broader than in the loop-legs suggesting the loop-tops are not sites of enhanced turbulence. Line-of-sight speeds in the loop arcade are typically $<10$ km s$^{-1}$, and mean non-thermal motions fall from 43 km s$^{-1}$ at the flare peak to 26 km s$^{-1}$ six minutes later. If the average velocity in the loop arcade is assumed to be at rest, then it implies a new reference wavelength for the Fe XXI line of $1354.106pm 0.023$ AA.
A small blowout jet was observed at the boundary of the south polar coronal hole on 2011 February 8 at around 21:00 UT. Images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) revealed an expanding loop rising
from one footpoint of a compact, bipolar bright point. Magnetograms from the Helioseismic Magnetic Imager (HMI) on board SDO showed that the jet was triggered by the cancelation of a parasitic positive polarity feature near the negative pole of the bright point. The jet emission was present for 25 mins and it extended 30 Mm from the bright point. Spectra from the EUV Imaging Spectrometer on board Hinode yielded a temperature and density of 1.6 MK and 0.9-1.7 x 10^8 cm^-3 for the ejected plasma. Line-of-sight velocities reached up to 250 km/s and were found to increase with height, suggesting plasma acceleration within the body of the jet. Evidence was found for twisting motions within the jet based on variations of the LOS velocities across the jet width. The derived angular speed was in the range 9-12 x 10^-3 rad s^-1, consistent with previous measurements from jets. The density of the bright point was 7.6 x 10^8 cm^-3, and the peak of the bright points emission measure occurred at 1.3 MK, with no plasma above 3 MK.
A blowout jet occurred within the south coronal hole on 9 February 2011 at 09:00 UT and was observed by the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory, and the EUV Imaging Spec
trometer (EIS) and X-Ray Telescope (XRT) onboard the Hinode spacecraft during coronal hole monitoring performed as part of Hinode Operations Program No. 177. Images from AIA show expanding hot and cold loops from a small bright point with plasma ejected in a curtain up to 30 Mm wide. The initial intensity front of the jet had a projected velocity of 200 km/s and line-of-sight (LOS) velocities measured by EIS are between 100 and 250 km/s. The LOS velocities increased along the jet, implying an acceleration mechanism operating within the body of the jet. The jet plasma had a density of 2.7 x 10^8 cm^-3, and a temperature of 1.4 MK. During the event a number of bright kernels were seen at the base of the bright point. The kernels have sizes of about 1000 km, are variable in brightness, and have lifetimes of 1-15 minutes. An XRT filter ratio yields temperatures of 1.5-3.0 MK for the kernels. The bright point existed for at least ten hours, but disappeared within two hours after the jet, which lasted for 30 minutes. HMI data reveal converging photospheric flows at the location of the bright point, and the mixed polarity magnetic flux canceled over a period of four hours on either side of the jet.
These notes discuss, in a style intended for physicists, how to average data and fit it to some functional form. I try to make clear what is being calculated, what assumptions are being made, and to give a derivation of results rather than just quote
them. The aim is put a lot useful pedagogical material together in a convenient place. This manuscript is a substantial enlargement of lecture notes I prepared for the Bad Honnef School on Efficient Algorithms in Computational Physics, September 10-14, 2012.
We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which the critical
behavior is very similar to that of the short-range model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the four-dimensional case.
We test for the presence or absence of the de Almeida-Thouless line using one-dimensional power-law diluted Heisenberg spin glass model, in which the rms strength of the interactions decays with distance, r as 1/r^{sigma}. It is argued that varying t
he power sigma is analogous to varying the space dimension d in a short-range model. For sigma=0.6, which is in the mean field regime regime, we find clear evidence for an AT line. For sigma = 0.85, which is in the non-mean-field regime and corresponds to a space dimension of close to 3, we find no AT line, though we cannot rule one out for very small fields. Finally for sigma=0.75, which is in the non-mean-field regime but closer to the mean-field boundary, the evidence suggests that there is an AT line, though the possibility that even larger sizes are needed to see the asymptotic behavior can not be ruled out.
We use Monte Carlo simulations to study the one-dimensional long-range diluted Heisenberg spin glass with interactions that fall as a power, sigma, of the distance. Varying the power is argued to be equivalent to varying the space dimension of a shor
t-range model. We are therefore able to study both the mean-field and non-mean-field regimes. For one value of sigma, in the non-mean-field regime, we find evidence that the chiral glass transition temperature may be somewhat higher than the spin glass transition temperature. For the other values of sigma we see no evidence for this.
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models studied, the har
dest for WalkSAT is the one for which there is a polynomial time algorithm.
We study the typical (median) value of the minimum gap in the quantum version of the Exact Cover problem using Quantum Monte Carlo simulations, in order to understand the complexity of the quantum adiabatic algorithm (QAA) for much larger sizes than
before. For a range of sizes, N <= 128, where the classical Davis-Putnam algorithm shows exponential median complexity, the QAA shows polynomial median complexity. The bottleneck of the algorithm is an isolated avoided crossing point of a Landau-Zener type (collision between the two lowest energy levels only).
