Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice

We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $\tau$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of $d_B$ = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent $\alpha = D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 - \tau)$ = 1.56(8). This result is compared with that obtained from a power spectrum analysis of the surface roughness, which yields $\alpha$ = 0.42(3) and $z$ = 1.5(1) in excellent agreement with those obtained from the scaling relations.Comment: 7 pages, 8 figures, accepted for publication in PR

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

A second-order singular boundary value problem

AbstractWe study the second-order boundary value problem −″(t) = α(t)f(u(t)), o < t < 1, satisfying αu(0) − βu″(0) = 0,γu(1) + δu″(1) = 0, where a(t) = Πi=1n ai(t) and α, β, γ, δ ≥ 0, αγ + αδ + βγ > 0. We assume that each ai(t) ϵ LPi [0, 1] for pi ≥ 1 and that each ai(t) has a singularity in (0, 1). To show the existence of countably many positive solutions, we apply Hölder's inequality and Krasnosel'skii∪'s fixed-point theorem for operators on a cone

Instantaneous positions of microwave solar bursts: Properties and validity of the multiple beam observations

The multiple beam technique determine burst sources positions when their angular extent are small compared with the beam shapes. We show for the first time that we can check the above condition with the simultaneous observation using at least four beams. The developed technique is not critically dependent on source shapes. By means of simulations we found that for narrow 1 arcmin long sources the uncertainties in position determination are less than 5 arcsec, and much better for symmetrical sources. The influence of side lobes on source positions determinations was found to be negligible. A qualitative method was developed when data from only three beams are available. Both methods are applied to the analysis of a solar burst observed with multiple beams at 48 GHz with the Itapetinga 13.7 m antenna. The multiple beam technique also offers the unique advantage to determine flux density irrespectively from the position displacements of the source with respect to the beams, or vice versa