Measurement of cathode spot parameters with pulsed laserdiagnostics

The cathode spot formation in air within the first 170 ns was investigated by laser absorption photography and ps-pulse interferometry. The discharge was initiated between electrodes made from Ag or Pd with cathode-anode distance below 300 μm, the arc duration was some milliseconds, and the arc current 5-10 A. Picosecond holographic interferometry and momentary absorption photography yielded spatial-temporal density distributions in the ignition phase of the cathode spot. An absolute electron density value on the order of 4×10²⁶ m^-3 has been found. In contrast to vacuum, the cathode spot plasmas broaden little with increasing distance from the cathode, thus narrow plasma channels are observed in the vicinity of the cathode surface having diameters <20 μm     

On the integrability of hyperbolic systems of riccati-type equations

We consider equations of the form U_xy = U * U_x, where U(x, y) is a function taking values in an arbitrary finite-dimensional algebra T over the field ℂ. We show that every such equation can be naturally associated with two characteristic Lie algebras, L_x and L_y. We define the notion of a ℤ-graded Lie algebraB corresponding to a given equation. We prove that for every equation under consideration, the corresponding algebraB can be taken as a direct sum of the vector spaces L_x and L_y if we define the commutators of the elements from L_x and L_y by means of the zero-curvature relations. Assuming that the algebra T has no left ideals, we classify the equations of the specified type associated with the finite-dimensional characteristic Lie algebras L_x and L_y. All of these equations are Darboux-integrable. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 2, pp. 261–275, November, 1997.     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

The effect of radiofrequency modulation of 57Fe hyperfine interaction by rotating magnetic field

The effect of ⁵⁷Fe hyperfine interaction radiofrequency (rf) modulation by external rotating magnetic field was studied in thin Permalloy foil by means of Mössbauer spectroscopy. The rf effect was investigated as a function of intensity for several rf field frequencies. The experiments show that the external rotating rf field causes considerable changes in the hyperfine pattern. The obtained spectra are in disagreement with those obtained by Perlow [Phys. Rev. 172 (1968) 319]. They also are inconsistent with magnetostriction hypothesis. Proceeding from the Mössbauer spectrum analysis one may conclude that the magnetization of investigated foil changes its direction in a complex manner. However, the undertaken experiments show that the essential number of Mössbauer nuclei experience the rotating magnetic field influence.     

Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Success and survival of operational research groups—A review

Operational Research groups were established in private and public sector organizations following on from their success supporting the military in the Second World War. In the early years their numbers grew rapidly but by the mid-1970s evidence started to accumulate that they were being viewed less favourably. Many organizations chose not to set up OR groups. Established groups were closed down or dispersed to operating units in organizations, particularly during the recessionary periods. In 1993 following on the closures of some major OR groups in the UK, the Operational Research Society decided to fund research to examine those factors influencing a group's success and survival. This review, which forms part of the research, first examines the history of OR groups in the UK and North America, arguing that in practice they were one of a number of internal organizational consultancies. As such they were judged by their competitive performance. Despite the intent of the founding fathers of OR many groups found their scope was limited to mainly tactical problems using analytical model based approaches although there were exceptions that were successful in making major contributions at the strategic level also. Within their chosen fields of activity however many groups flourished whilst some failed. This review presents a comprehensive list of influences on success and survival. They include changes in the external environment, together with shifts in managerial style and culture, organizational factors, and the OR group itself. The review concludes that, while OR groups can do much to protect themselves from closure, organizational changes within a hostile managerial culture demand a creative response that acknowledges new requirements. Areas where an OR group has greatest influence over its effectiveness include its leadership and personnel, project balance and management. In addition, to be successful OR groups need to positively develop and market their services in an increasingly competitive managerial climate.     

Thermal diffusivity measurements in porous ceramics by photothermal methods

Received: 16 September 1996/Accepted: 6 January 1997     

Twistor Geometry for Hyperkähler Metrics on Complex Adjoint Orbits

We study the hyperkähler geometry of complex adjoint orbits from the point of view of twistor theory. We introduce, for complex semisimple adjoint orbits, the associated spectral curve and construct the twistor space as a union of certain regular adjoint orbits; we also exhibit the family of twistor lines. Furthermore, we show how our methods may be applied for describing hyperkähler metrics associated to more general spectral curves. In particular, we give an algebraic characterisation of the twistor lines.