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.

Observation of Collisionless Shocks in Laser-Plasma Experiments

The propagation in a rarefied plasma (n(e)less than or similar to 10(15) cm(-3)) of collisionless shock waves and ion-acoustic solitons, excited following the interaction of a long (tau(L)similar to 470 ps) and intense (I similar to 10(15) W cm(-2)) laser pulse with solid targets, has been investigated via proton probing techniques. The shocks' structures and related electric field distributions were reconstructed with high spatial and temporal resolution. The experimental results were interpreted within the framework of the nonlinear wave description based on the Korteweg-de Vries-Burgers equation.

Electrostatic shock dynamics in superthermal plasmas

The propagation of ion acoustic shocks in nonthermal plasmas is investigated, both analytically and numerically. An unmagnetized collisionless electron-ion plasma is considered, featuring a superthermal (non-Maxwellian) electron distribution, which is modeled by a ?-(kappa) distribution function. Adopting a multiscale approach, it is shown that the dynamics of low-amplitude shocks is modeled by a hybrid Korteweg-de Vries-Burgers (KdVB) equation, in which the nonlinear and dispersion coefficients are functions of the ? parameter, while the dissipative coefficient is a linear function of the ion viscosity. All relevant shock parameters are shown to depend on ?: higher deviations from a pure Maxwellian behavior induce shocks which are narrower, faster, and of larger amplitude. The stability profile of the kink-shaped solutions of the KdVB equation against external perturbations is investigated. The spatial profile of the shocks is found to depend upon the dispersion and the dissipation term, and the role of the interplay between dispersion and dissipation is elucidated.

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).

Nonlinear dynamics of multidimensional electrostatic excitations in nonthermal plasmas

Electrostatic solitary waves in plasmas are the focus of many current studies of localized electrostatic disturbances in both laboratory and astrophysical plasmas. Motivated by recent experimental observations, in which electrostatic solitary structures were detected in laser-plasma experiments, we have undertaken an investigation of the nonlinear dynamics of plasma evolving in two dimensions, in the presence of excess superthermal background electrons. We investigate the effect of a magnetic field on weakly nonlinear ion-acoustic waves. Deviation from the Maxwellian distribution is effectively modelled by the kappa model. A linear dispersion relation is derived, and a decrease in frequency and phase speed in both parallel and perpendicular modes can be seen, which is due to excess superthermal electrons, and which is stronger in the upper mode, and hardly noticeable in the lower (acoustic) mode. We show that ion-acoustic solitary waves can be generated during the nonlinear evolution of a plasma fluid, and their nonlinear propagation is governed by a Zakharov-Kuznetsov (ZK) type equation. A multiple scales perturbation technique is used to derive the ZK equation. Shock excitations can be produced if we allow for dissipation in the model, resulting in a Zakharov-Kuznetsov Burgers type equation. Different types of shock solutions and solitary waves are obtained, depending on the relation between the system parameters, and the effect of these on electrostatic shock structures is investigated numerically. A parametric investigation is conducted into the role of plasma nonthermality and magnetic field strength. © 2013 IOP Publishing Ltd.

Twinning anisotropy of tantalum during nanoindentation

Unlike other BCC metals, the plastic deformation of nanocrystalline Tantalum during compression is regulated by deformation twinning. Whether or not this twinning exhibits anisotropy was investigated through simulation of displacement-controlled nanoindentation test using molecular dynamics simulation. MD data was found to correlate well with the experimental data in terms of surface topography and hardness measurements. The mechanism of the transport of material was identified due to the formation and motion of prismatic dislocations loops (edge dislocations) belonging to the 1/2<111> type and <100> type Burgers vector family. Further analysis of crystal defects using a fully automated dislocation extraction algorithm (DXA) illuminated formation and migration of twin boundaries on the (110) and (111) orientation but not on the (010) orientation and most importantly after retraction all the dislocations disappeared on the (110) orientation suggesting twinning to dominate dislocation nucleation in driving plasticity in tantalum. A significant finding was that the maximum shear stress (critical Tresca stress) in the deformation zone exceeded the theoretical shear strength of tantalum (Shear modulus/ 2π~10.03 GPa) on the (010) orientation but was lower than it on the (110) and the (111) orientations. In light to this, the conventional lore of assuming the maximum shear stress being 0.465 times the mean contact pressure was found to break down at atomic scale.

Measurements of immune responses for establishing correlates of vaccine protection against HIV

Well-defined correlates of protective immunity are an essential component of rational vaccine development. Despite years of basic science and three HIV vaccine efficacy trials, correlates of immunological protection from HIV infection remain undefined. In December 2010, a meeting of scientists engaged in basic and translational work toward developing HIV-1 vaccines was convened. The goal of this meeting was to discuss current opportunities and optimal approaches for defining correlates of protection, both for ongoing and future HIV-1 vaccine candidates; specific efforts were made to engage young scientists. We discuss here the highlights from the meeting regarding the progress made and the way forward for a protective HIV-1 vaccine.

Dust-acoustic shocks in strongly coupled dusty plasmas

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.