On the influence that the ground electrode diameter has in the propulsion efficiency of an asymmetric capacitor in nitrogen gas

In this work the propulsion force developed in an asymmetric capacitor will be calculated for three different diameters of the ground electrode. The used ion source is a small diameter wire, which generates a positive corona discharge in nitrogen gas directed to the ground electrode. By applying the fluid dynamic and electrostatic theories all hydrodynamic and electrostatic forces that act on the considered geometries will be computed in an attempt to provide a physical insight on the force mechanism that acts on the asymmetrical capacitors, and also to understand how to increase the efficiency of propulsion.Comment: 13 pages, 8 figures, Accepted for publication in "Physics of Plasmas

Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters

We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the 6N-dimensional phase space Omega of the relativistic systems with 2N particles and N antiparticles, there exists a 2N-dimensional Poincaré-invariant submanifold OmegaP corresponding to N free particles and N bound particle-antiparticle pairs in their ground state. The Tzitzeica N-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of OmegaP. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state

Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice

It is shown that some special reduction of infinite 1D Toda lattice gives differential constraints compatible with the Kaup -- Broer system. A family of the travelling wave solutions of the Kaup -- Broer system and its higher version is constructed.Comment: LaTeX, uses IOP styl

Conservation laws and normal forms of evolution equations

We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation, Korteweg-de-Vries-type equations, and Schwarzian KdV equation. It is also shown that for linear evolution equations all their conservation laws are (modulo trivial conserved vectors) at most quadratic in the dependent variable and its derivatives.Comment: 16 page