Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

Electron-scale electrostatic solitary waves and shocks: the role of superthermal electrons

The propagation of electron-acoustic solitary waves and shock structures is investigated in a plasma characterized by a superthermal electron population. A three-component plasma model configuration is employed, consisting of inertial (“cold”) electrons, inertialess ? (kappa) distributed superthermal (“hot”) electrons and stationary ions. A multiscale method is employed, leading to a Korteweg-de Vries (KdV) equation for the electrostatic potential (in the absence of dissipation). Taking into account dissipation, a hybrid Korteweg-de Vries-Burgers (KdVB) equation is derived. Exact negative-potential pulse- and kink-shaped solutions (shocks) are obtained. The relative strength among dispersion, nonlinearity and damping coefficients is discussed. Excitations formed in superthermal plasma (finite ?) are narrower and steeper, compared to the Maxwellian case (infinite ?). A series of numerical simulations confirms that energy initially stored in a solitary pulse which propagates in a stable manner for large ? (Maxwellian plasma) may break down to smaller structures or/and to random oscillations, when it encounters a small-? (nonthermal) region. On the other hand, shock structures used as initial conditions for numerical simulations were shown to be robust, essentially responding to changed in the environment by a simple profile change (in width).

Cold, Hungry and Scared:Prison Films About the Troubles

The cinematic representations of the prison experience during the Northern Irish Troubles.

Effect of offset web holes on web crippling strength of cold-formed steel channel sections under end-two-flange loading condition

A combination of experiments and non-linear finite element analyses are used to investigate the effect of offset web holes on the web crippling strength of cold-formed steel channel sections under the end-two-flange (ETF) loading condition; the cases of both flanges fastened and unfastened to the support are considered. The web holes are located at the mid-depth of the sections, with a horizontal clear distance of the web holes to the near edge of the bearing plate. Finite element analysis results are compared against the laboratory test results; good agreement was obtained in terms of both strength and failure modes. A parametric study was then undertaken to investigate both the effect of the position of holes in the web and the cross-section sizes on the web crippling strength of the channel sections. It was demonstrated that the main factors influencing the web crippling strength are the ratio of the hole depth to the depth of the web, and the ratio of the distance from the edge of the bearing to the flat depth of the web. Design recommendations in the form of web crippling strength reduction factors are proposed in this study.

Shock avoidance by discrimination learning in the shore crab (Carcinus maenas) is consistent with a key criterion for pain

Nociception allows for immediate reflex withdrawal whereas pain allows for longer-term protection via rapid learning. We examine here whether shore crabs placed within a brightly lit chamber learn to avoid one of two dark shelters when that shelter consistently results in shock. Crabs were randomly selected to receive shock or not prior to making their first choice and were tested again over 10 trials. Those that received shock in trial 2, irrespective of shock in trial 1, were more likely to switch shelter choice in the next trial and thus showed rapid discrimination. During trial 1, many crabs emerged from the shock shelter and an increasing proportion emerged in later trials, thus avoiding shock by entering a normally avoided light area. In a final test we switched distinctive visual stimuli positioned above each shelter and/or changed the orientation of the crab when placed in the chamber for the test. The visual stimuli had no effect on choice, but crabs with altered orientation now selected the shock shelter, indicating that they had discriminated between the two shelters on the basis of movement direction. These data, and those of other recent experiments, are consistent with key criteria for pain experience and are broadly similar to those from vertebrate studies. © 2013. Published by The Company of Biologists Ltd.

Generation of scaled protogalactic seed magnetic fields in laser-produced shock waves

The standard model for the origin of galactic magnetic fields is through the amplification of seed fields via dynamo or turbulent processes to the level consistent with present observations. Although other mechanisms may also operate, currents from misaligned pressure and temperature gradients (the Biermann battery process) inevitably accompany the formation of galaxies in the absence of a primordial field. Driven by geometrical asymmetries in shocks associated with the collapse of protogalactic structures, the Biermann battery is believed to generate tiny seed fields to a level of about 10 gauss (refs 7, 8). With the advent of high-power laser systems in the past two decades, a new area of research has opened in which, using simple scaling relations, astrophysical environments can effectively be reproduced in the laboratory. Here we report the results of an experiment that produced seed magnetic fields by the Biermann battery effect. We show that these results can be scaled to the intergalactic medium, where turbulence, acting on timescales of around 700 million years, can amplify the seed fields sufficiently to affect galaxy evolution.

Cold War Politics in Britain and the Contested Legacy of the Spanish Civil War

This article offers a sustained examination of how the vicissitudes of the Cold War shaped changing interpretations of the Spanish Civil War in Britain. Considering the perspectives of participants and historians, it focuses on the diverse strands of the Left that frequently drew on the civil war to attack each other and to make wider arguments about the global Cold War. First, with the aim of criticizing Communist take-overs in Eastern Europe in the late 1940s, the article analyzes retrospective assaults on Communist party tactics and Soviet foreign policy in Spain. Second, in order to argue that the Soviet Union took a counter-revolutionary line after 1956, it investigates the re-emergence of debates over the Spanish revolution. Third, to express disapproval of the United States, it examines the increasing use of the civil war as an analogy in Cold War international affairs from the 1960s. Fourth, in support of non-Soviet Left-of-Centre collaboration, most notably Eurocommunism in the 1970s and opposition to Margaret Thatcher’s Conservative government in the 1980s, it considers the renewed emphasis on the popular front. The trajectories of these debates reveal that, over time, the weight of the Left’s criticism moved from the Soviet Union towards the United States.

Cold comfort at the Magh Mela: Social identity processes and physical hardship

Humans inhabit environments that are both social and physical, and in this article weinvestigate if and how social identity processes shape the experience and negotiation ofphysically demanding environmental conditions. Specifically, we consider how severe coldcan be interpreted and experienced in relation to group members’ social identity. Ourdata comprise ethnographic observation and semi-structured interviews with pilgrimsattending a month-long winter Hindu religious festival that is characterized bynear-freezing conditions. The analysis explores (1) how pilgrims appraised the cold andhow these appraisals were shaped by their identity as pilgrims; (2) how shared identitywith other pilgrims led to forms of mutual support that made it easier to cope with thecold. Our findings therefore extend theorizing on social identity processes to highlighttheir relevance to physical as well as social conditions.

Time-Resolved Characterization of the Formation of a Collisionless Shock

We report on the temporally and spatially resolved detection of the precursory stages that lead to the formation of an unmagnetized, supercritical collisionless shock in a laser-driven laboratory experiment. The measured evolution of the electrostatic potential associated with the shock unveils the transition from a current free double layer into a symmetric shock structure, stabilized by ion reflection at the shock front. Supported by a matching particle-in-cell simulation and theoretical considerations, we suggest that this process is analogous to ion reflection at supercritical collisionless shocks in supernova remnants.

Universal behaviour of shock precursors in the presence of efficient cosmic ray acceleration

The self-consistent interaction between energetic particles and self-generated hydromagnetic waves in a cosmic ray pressure dominated plasma is considered. Using a three-dimensional hybrid magnetohydrodynamics (MHD)-kinetic code, which utilizes a spherical harmonic expansion of the Vlasov-Fokker-Planck equation, high-resolution simulations of the magnetic field growth including feedback on the cosmic rays are carried out. It is found that for shocks with high cosmic ray acceleration efficiency, the magnetic fields become highly disorganized, resulting in near isotropic diffusion, independent of the initial orientation of the ambient magnetic field. The possibility of sub-Bohm diffusion is demonstrated for parallel shocks, while the diffusion coefficient approaches the Bohm limit from below for oblique shocks. This universal behaviour suggests that Bohm diffusion in the root-mean-squared field inferred from observation may provide a realistic estimate for the maximum energy acceleration time-scale in young supernova remnants. Although disordered, the magnetic field is not self-similar suggesting a non-uniform energy-dependent behaviour of the energetic particle transport in the precursor. Possible indirect radiative signatures of cosmic ray driven magnetic field amplification are discussed.

Diffusive shock acceleration at laser-driven shocks: studying cosmic-ray accelerators in the laboratory

The non-thermal particle spectra responsible for the emission from many astrophysical systems are thought to originate from shocks via a first order Fermi process otherwise known as diffusive shock acceleration. The same mechanism is also widely believed to be responsible for the production of high energy cosmic rays. With the growing interest in collisionless shock physics in laser produced plasmas, the possibility of reproducing and detecting shock acceleration in controlled laboratory experiments should be considered. The various experimental constraints that must be satisfied are reviewed. It is demonstrated that several currently operating laser facilities may fulfil the necessary criteria to confirm the occurrence of diffusive shock acceleration of electrons at laser produced shocks. Successful reproduction of Fermi acceleration in the laboratory could open a range of possibilities, providing insight into the complex plasma processes that occur near astrophysical sources of cosmic rays.

STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION

Stationary solutions to the equations of nonlinear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean free path is thought to be an increasing function of energy, this condition is conventionally implemented as an upper cutoff in energy space-particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for the substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven nonresonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off-a diagnostic that is in principle accessible to observation.