Mitsch's order and inclusion for binary relations and partitions

Mitsch's natural partial order on the semigroup of binary relations is here characterised by equations in the theory of relation algebras. The natural partial order has a complex relationship with the compatible partial order of inclusion, which is explored by means of a sublattice of the lattice of preorders on the semigroup. The corresponding sublattice for the partition monoid is also described.Comment: 8 pages, 2 figure

Polarized Magnetic Wire Induced by Tunneling Through a Magnetic Impurity

Using the zero mode method we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent $\alpha(\leq 1)$. We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, the conductance as a function of temperature is $G \sim \frac{e^2}{h} (T/T_F)^{2(\alpha-2)}$, whereas for off-resonance conditions the conductance is $G \sim \frac{e^2}{h} (T/T_F)^{2(\alpha-1)}$. By applying a gate voltage and/or a magnetic field, one of the spin components can be in resonance while the other is off-resonance causing a strong asymmetry between the spin-up and spin-down conductances.Comment: 8 pages, submitted to PR

Plasma igniter for internal combustion engine

An igniter for the air/fuel mixture used in the cylinders of an internal combustion engine is described. A conventional spark is used to initiate the discharge of a large amount of energy stored in a capacitor. A high current discharge of the energy in the capacitor switched on by a spark discharge produces a plasma and a magnetic field. The resultant combined electromagnetic current and magnetic field force accelerates the plasma deep into the combustion chamber thereby providing an improved ignition of the air/fuel mixture in the chamber