English Trade Mark Law in the Eighteenth Century: Blanchard v Hill Revisited - Another 'Case of Monopolies'?

The decision of Lord Hardwicke LC in Blanchard v Hill in 1742 is the earliest reported case on the equitable jurisdiction to grant injunctive relief against trade mark piracy. The ambiguous manner in which the case was reported led to the decision being interpreted as either the basis of equitable jurisdiction or a denial of jurisdiction. This article seeks to establish the background to the case, what actually happened, and the immediate impact of the decision. The scene is set, however, in a parallel symbolic universe – heraldry – because in 1740, the officers of arms were confronted with a trade mark case.

Instability and evolution of nonlinearly interacting water waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrodinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.

Instability and dynamics of two nonlinearly coupled laser beams in a plasma

The nonlinear interaction between two laser beams in a plasma is investigated in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schrodinger equations that are coupled with the slow plasma density response. A nonlinear dispersion relation is derived and used to study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations. (c) 2006 American Institute of Physics.

Modulational instability and localized excitations of dust-ion acoustic waves

Theoretical and numerical studies are carried out of the nonlinear amplitude modulation of dust-ion acoustic waves propagating in an unmagnetized weakly coupled plasma comprised of electrons, positive ions, and charged dust grains, considering perturbations oblique to the carrier wave propagation direction. The stability analysis, based on a nonlinear Schrodinger-type equation, exhibits a wide instability region, which depends on both the angle theta between the modulation and propagation directions and the dust number density n(d). Explicit expressions for the instability increment and threshold are obtained. The possibility and conditions for the existence of different types of localized excitations are also discussed. (C) 2003 American Institute of Physics.

One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.