Fast computation of Bernoulli, Tangent and Secant numbers

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).Comment: 16 pages. To appear in Computational and Analytical Mathematics (associated with the May 2011 workshop in honour of Jonathan Borwein's 60th birthday). For further information, see http://maths.anu.edu.au/~brent/pub/pub242.htm

Current State of the Electrodynamic Dust Shield for Mitigation

The Electrodynamic Dust Shield (EDS) has been developed as a means to lift, transport and remove dust from surfaces for over 18 years in the Electrostatics and Surface Physics Laboratory at NASA Kennedy Space Center. Resent advances in the technology have allowed large-scale EDSs to be fabricated using roll-to-roll techniques for quick efficient processing. The aim of the current research is to demonstrate the 3-dimensional (3-D) version of the EDS and its applicability to various surfaces of interest throughout the Artemis program that require dust mitigation. The conventional two dimensional (2-D) EDS has been comprised of interdigitated electrodes across a surface of alternating polarity to setup non-uniform electric fields in the location of interest for which the particles need to be removed. The 2-D system can be designed to accommodate various phases. For example, the two phase EDS is comprised of two electrodes 180 out of phase, while the 3-phase EDS is 120 out of phase with the adjacent leg. 4-phase EDS configurations are also possible but for each square wave a high voltage signal is applied to each leg

Temperature-controlled interlayer exchange coupling in strong/weak ferromagnetic multilayers: a thermo-magnetic Curie-switch

We investigate a novel type of interlayer exchange coupling based on driving a strong/weak/strong ferromagnetic tri-layer through the Curie point of the weakly ferromagnetic spacer, with the exchange coupling between the strongly ferromagnetic outer layers that can be switched, on and off, or varied continuously in magnitude by controlling the temperature of the material. We use Ni-Cu alloy of varied composition as the spacer material and model the effects of proximity-induced magnetism and the interlayer exchange coupling through the spacer from first principles, taking into account not only thermal spin-disorder but also the dependence of the atomic moment of Ni on the nearest-neighbor concentration of the non-magnetic Cu. We propose and demonstrate a gradient-composition spacer, with a lower Ni-concentration at the interfaces, for greatly improved effective-exchange uniformity and significantly improved thermo-magnetic switching in the structure. The reported magnetic multilayer materials can form the base for a variety of novel magnetic devices, such as sensors, oscillators, and memory elements based on thermo-magnetic Curie-switching in the device.Comment: 15 pages, 5 figure

Germanium Detector with Internal Amplification for Investigation of Rare Processes

Device of new type is suggested - germanium detector with internal amplification. Such detector having effective threshold about 10 eV opens up fresh opportunity for investigation of dark matter, measurement of neutrino magnetic moment, of neutrino coherent scattering at nuclei and for study of solar neutrino problem. Construction of germanium detector with internal amplification and perspectives of its use are described.Comment: 13 pages, latex, 3 figures, report at NANP-99, International Conference on Non-Accelerator Physics, Dubna, Russia, June 29- July 3, 1999. To be published in the Proceeding

In Situ Test Method for the Electrostatic Characterization of Lunar Dust

This paper serves to illustrate the testing methods necessary to classify the electrostatic properties of lunar dust using in situ instrumentation and the required techniques therein. A review of electrostatic classification of lunar simulant materials is provided as is its relevance to the success of future human lunar missions

Entropic phase separation of linked beads

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase separation mechanism of the system is extremely robust and does not depend on the particlular physical realization of the network. The discussed model applies as well to other polymer linked particle aggregates, such as nano-particles connected with short DNA linkers

Fluvial Volumes, Timescales, and Intermittency in Milna Crater, Mars

Ancient lake deposits and valley networks on Mars provide strong evidence that its surface was once modified by liquid water, but the extent of that modification is still debated. Ancient lacustrine deposits in Milna Crater provide insight into the timescale and fluid volume required to construct fluvially derived sedimentary deposits near the Noachian-Hesperian boundary. Placing the lacustrine deposits their regional context in Paran Valles provides a quantitative measurement of the intermittency of large, water-mediated sediment transport events in that region

Effect of Non-Magnetic Impurities (Zn,Li) in a Hole Doped Spin-Fermion Model for Cuprates

The effect of adding non-magnetic impurities (NMI), such as Zn or Li, to high-Tc cuprates is studied applying Monte Carlo techniques to a spin-fermion model. It is observed that adding Li is qualitatively similar to doping with equal percentages of Sr and Zn. The mobile holes (MH) are trapped by the NMI and the system remains insulating and commensurate with antiferromagnetic (AF) correlations. This behavior persists in the region %NMI > %MH. On the other hand, when %NMI < %MH magnetic and charge incommensurabilities are observed. The vertical or horizontal hole-rich stripes, present when % NMI=0 upon hole doping, are pinned by the NMI and tend to become diagonal, surrounding finite AF domains. The %MH-%NMI plane is investigated. Good agreement with experimental results is found in the small portion of this diagram where experimental data are available. Predictions about the expected behavior in the remaining regions are made.Comment: Four pages with four figures embedded in tex