Stirling cycle cryogenic cooler

A long lifetime Stirling cycle cryogenic cooler particularly adapted for space applications is described. It consists of a compressor section centrally aligned end to end with an expansion section, and respectively includes a reciprocating compressor piston and displacer radially suspended in interconnecting cylindrical housings by active magnetic bearings and has adjacent reduced clearance regions so as to be in noncontacting relationship therewith and wherein one or more of these regions operate as clearance seals. The piston and displacer are reciprocated in their housings by linear drive motors to vary the volume of respectively adjacent compression and expansion spaces which contain a gaseous working fluid and a thermal regenerator to effect Stirling cycle cryogenic cooling

Bernoulli numbers and solitons

We present a new formula for the Bernoulli numbers as the following integral $$B_{2m} =\frac{(-1)^{m-1}}{2^{2m+1}} \int_{-\infty}^{+\infty} (\frac{d^{m-1}}{dx^{m-1}} {sech}^2 x)^2dx.$$ This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory.Comment: 5 page

The 'Square Root' of the Interacting Dirac Equation

The 'square root' of the interacting Dirac equation is constructed. The obtained equations lead to the Yang-Mills superfield with the appropriate equations of motion for the component fields.Comment: 6 page

The dynamical equation of the spinning electron

We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when quantised. It is shown that the dynamics can be described in terms of the evolution of the point charge which satisfies a fourth order differential equation or, alternatively, as a system of second order differential equations by describing the evolution of both the center of mass and center of charge of the particle. As an application of the found dynamical equations, the Coulomb interaction between two spinning electrons is considered. We find from the classical viewpoint that these spinning electrons can form bound states under suitable initial conditions. Since the classical Coulomb interaction of two spinless point electrons does not allow for the existence of bound states, it is the spin structure that gives rise to new physical phenomena not described in the spinless case. Perhaps the paper may be interesting from the mathematical point of view but not from the point of view of physics.Comment: Latex2e, 14 pages, 5 figure

Spatiotemporal instability of a confined capillary jet

Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this work, we present an extensive analytical, numerical and experimental analysis of confined capillary jets extending previous studies. We propose an extended, accurate analytic model in the limit of low Reynolds flows, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show a remarkable accuracy with results from the extensive experimental exploration provided.Comment: Submitted to the Physical Review E (20-March-2008

Luttinger States at the Edge

An effective wavefunction for the edge excitations in the Fractional quantum Hall effect can be found by dimensionally reducing the bulk wavefunction. Treated this way the Laughlin $\nu=1/(2n+1)$ wavefunction yields a Luttinger model ground state. We identify the edge-electron field with a Luttinger hyper-fermion operator, and the edge electron itself with a non-backscattering Bogoliubov quasi-particle. The edge-electron propagator may be calculated directly from the effective wavefunction using the properties of a one-dimensional one-component plasma, provided a prescription is adopted which is sensitive to the extra flux attached to the electrons

Can useful toroidal current be driven by classical viscoresistive Alfvén waves?

Simple, yet exact, analytic solutions for the shear and compressional Alfvén wave are obtained for helical magnetohydrodynamic (MHD) waves in cylindrical geometry with both resistivity and viscosity included. The current driven by all possible combinations of these waves is examined in the quasilinear regime (i.e., where the magnetic field produced by the driven current is not self-consistently included in the equilibrium where the wave equations are derived). It is found in all cases that it is not possible to drive significant bulk axial current with small amplitude wave fields. Thus, any useful low-frequency current drive scheme will have to be based on phenomena more complicated than those discussed here