Signatures of the self-modulation instability of relativistic proton bunches in the AWAKE experiment

We investigate numerically the detection of the self-modulation instability in a virtual detector located downstream from the plasma in the context of AWAKE. We show that the density structures, appearing in the temporally resolving virtual detector, map the transverse beam phase space distribution at the plasma exit. As a result, the proton bunch radius that appears to grow along the bunch in the detector results from the divergence increase along the bunch, related with the spatial growth of the self-modulated wakefields. In addition, asymmetric bunch structures in the detector are a result of asymmetries of the bunch divergence, and do not necessarily reflect asymmetric beam density distributions in the plasma.Comment: Accepted for publication in NIM-A for the proceedings of the 3rd European Advanced Accelerator Workshop. 5 pages, 2 figure

Whipped oil stabilised by surfactant crystals

We describe a protocol for preparing very stable air-in-oil foams starting with a one-phase oil solution of a fatty acid (myristic acid) in high oleic sunflower oil at high temperature. Upon cooling below the solubility limit, a two-phase mixture consisting of fatty acid crystals (length around 50 μm) dispersed in an oil solution at its solubility is formed which, after whipping, coat air bubbles in the foam. Foams which do not drain, coalesce or coarsen may be produced either by increasing the fatty acid concentration at fixed temperature or aerating the mixtures at different temperatures at constant concentration. We prove that molecular fatty acid is not surface-active as no foam is possible in the one-phase region. Once the two-phase region is reached, fatty acid crystals are shown to be surface-active enabling foam formation, and excess crystals serve to gel the continuous oil phase enhancing foam stability. A combination of rheology, X-ray diffraction and pulsed nuclear magnetic resonance is used to characterise the crystals and oil gels formed before aeration. The crystal-stabilised foams are temperature-sensitive, being rendered completely unstable on heating around the melting temperature of the crystals. The findings are extended to a range of vegetable oil foams stabilised by a combination of adsorbed crystals and gelling of the oil phase, which destabilise at different temperatures depending on the composition and type of fatty acid chains in the triglyceride molecules

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order-parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics.Comment: 5 pages, 3 figures; published versio

Exponential Distributions in a Mechanical Model for Earthquakes

We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment), time duration and number of blocks involved in an event show that exponential distributions are found in a given range of the paramenter space. This occurs when the two kinds of springs present in the model have the same, or approximately the same, value for the elastic constants. Exponential distributions have also been seen recently in an experimental system to model earthquake-like dynamics [M. A. Rubio and J. Galeano, {\sl Phys. Rev. E} {\bf 50}, 1000 (1994)].Comment: 11 pages, uuencoded (submitted to Phys. Rev. E