Triangle in a brick

In this paper we shall investigate the following problem: Which is the largest regular triangle in a brick with volume 1 and having edge lengthes greater than $\frac{1}{\sqrt{2}}$? We prove that there are three optimal cases in all which the edge lengthes of the triangles are $\sqrt{2}$, respectively.Comment: 6 pages, 4 figure

The duration distribution of Swift Gamma-Ray Bursts

Decades ago two classes of gamma-ray bursts were identified and delineated as having durations shorter and longer than about 2 s. Subsequently indications also supported the existence of a third class. Using maximum likelihood estimation we analyze the duration distribution of 888 Swift BAT bursts observed before October 2015. Fitting three log-normal functions to the duration distribution of the bursts provides a better fit than two log-normal distributions, with 99.9999% significance. Similarly to earlier results, we found that a fourth component is not needed. The relative frequencies of the distribution of the groups are 8% for short, 35% for intermediate and 57% for long bursts which correspond to our previous results. We analyse the redshift distribution for the 269 GRBs of the 888 GRBs with known redshift. We find no evidence for the previously suggested difference between the long and intermediate GRBs' redshift distribution. The observed redshift distribution of the 20 short GRBs differs with high significance from the distributions of the other groups.Comment: accepte

Overlaps after quantum quenches in the sine-Gordon model

We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results are used to confirm the validity of a previously proposed analytical Ansatz for the initial state in the sinh-Gordon quench.Comment: 13 pages, 4 pdf figure

Defect related switching field reduction in small magnetic particle arrays

An array of 42 mum square, 3 mum thick garnet particles has been studied. The strong crystalline uniaxial anisotropy of these particles results in the stable remanent state being single domain with magnetization parallel to the film normal. Magneto-optic measurements of individual particles provide distribution statistics for the easy-axis switching field H-sw, and the in-plane hard-axis effective anisotropy field, H-eff, which induces the formation of a metastable stripe domain structure. Both H-sw and H-eff are much smaller than the crystalline anisotropy field. Micromagnetic simulations show that the small H-sw cannot be attributed to shape anisotropy, but is consistent with smooth, localized reductions in the crystalline anisotropy caused by defects in either the particles or the substrate

Mass spectrometric analysis of small negative ions (e/m < 100) produced by Trichel pulse negative corona discharge fed by ozonised air

Mass spectrometric analysis of small negative ions (e/m < 100) produced by DC negative corona discharge in ozonised wet air both in flow and flow-stopped regimes was conducted at pressure of 30 kPa. The point-to-plain electrode system has been used. The yield of individual ions is strongly affected by trace concentrations of ozone in both regimes. Ozone concentration greater than 25 ppm is sufficient to completely suppress the appearance of O2- and a NO2- ion as well as theirs clusters in the mass spectra. The temporal increase in concentration of NO3- ions and NO3-.(H2O)n (n = 1, 2) hydrated clusters was observed in flow-stopped regime accompanied by reduction in yield of CO3- ion and its water clusters CO3-.(H2O)n (n = 1, 2), which otherwise are the dominant ions in flowing wet air free of ozone. In contrast the addition of ozone into the flow of wet air resulted in evident increase in abundance of the clusters CO3-.(H2O)n (n = 1, 2). This is an evidence of an active role of nitrous oxide produced in flow-stopped regime in sufficient amount. The measured electrical conductivity of drift region confirmed the role of additional dissociative attachment of electrons by ozone molecules as well as a formation of clusters of lower mobility with increasing ozone concentration in the discharge gap