A singularity free analytical solution of artificial satellite motion with drag

The connection between the existing Delaunay-Similar and Poincare-Similar satellite theories in the true anomaly version is outlined for the J(2) perturbation and the new drag approach. An overall description of the concept of the approach is given while the necessary expansions and the procedure to arrive at the computer program for the canonical forces is delineated. The procedure for the analytical integration of these developed equations is described. In addition, some numerical results are given. The computer program for the algebraic multiplication of the Fourier series which creates the FORTRAN coding in an automatic manner is described and documented

Exceptional Circumstances Justifying Vacatur When Lower Court Decision Mooted by Settlement: Repeat Litigants Slide into Home with Second Circuit Decision - Major League Baseball Properties, Inc. v. Pacific Trading Cards, Inc.

At heart in the scholarship advocating Alternative Dispute Resolution are two interests: one, that using processes such as negotiation, mediation, and arbitration conserve public and private resources otherwise expended on litigation; and two, that in certain circumstances, these alternative processes may provide better justice than would occur in litigation.\u27 However, once litigation of a case has commenced, and an adverse judgment has been made against one party, that party may not be willing to settle the case unless the adverse judgement is vacated.4 Historically, most state and federal courts would routinely grant vacatur when requested by litigants who settled their disputes.\u27 Since the Supreme Court held in United States Bancorp Mortgage Co. v. Bonner Mall Partnership that federal courts should not vacate decisions mooted by settlement absent exceptional circumstances, federal courts have been reluctant to grant such requests.6 This presumption against vacatur arguable discourages settlement. It is against this backdrop that the Second Circuit considered the facts of Major League Baseball Properties, Inc. v. Pacific Trading Cards, Inc

An Analytical Satellite Orbit Predictor (ASOP)

The documentation and user's guide for the Analytical Satellite Orbit Predictor (ASOP) computer program is presented. The ASOP is based on mathematical methods that represent a new state-of-the-art for rapid orbit computation techniques. It is intended to be used for computation of near-earth orbits including those of the shuttle/orbiter and its payloads

The method of averages applied to the KS differential equations

A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution

Intercalation of graphene on SiC(0001) via ion-implantation

Electronic devices based on graphene technology are catching on rapidly and the ability to engineer graphene properties at the nanoscale is becoming, more than ever, indispensable. Here, we present a new procedure of graphene functionalization on SiC(0001) that paves the way towards the fabrication of complex graphene electronic chips. The procedure resides on the well-known ion-implantation technique. The efficiency of the working principle is demonstrated by the intercalation of the epitaxial graphene layer on SiC(0001) with Bi atoms, which was not possible following standard procedures. Our results put forward the ion-beam lithography to nanostructure and functionalize desired graphene chips

Rashba Effect at Magnetic Metal Surfaces

We give experimental and theoretical evidence of the Rashba effect at the magnetic rare-earth metal surface Gd(0001). The Rashba effect is substantially enhanced and the Rashba parameter changes its sign when a metal-oxide surface layer is formed. The experimental observations are quantitatively described by ab initio calculations that give a detailed account of the near-surface charge density gradients causing the Rashba effect. Since the sign of the Rashba splitting depends on the magnetization direction, the findings open up new opportunities for the study of surface and interface magnetism.Comment: 4 Fig

LEED Holography applied to a complex superstructure: a direct view of the adatom cluster on SiC(111)-(3x3)

For the example of the SiC(111)-(3x3) reconstruction we show that a holographic interpretation of discrete Low Energy Electron Diffraction (LEED) spot intensities arising from ordered, large unit cell superstructures can give direct access to the local geometry of a cluster around an elevated atom, provided there is only one such prominent atom per surface unit cell. By comparing the holographic images obtained from experimental and calculated data we illuminate validity, current limits and possible shortcomings of the method. In particular, we show that periodic vacancies such as cornerholes may inhibit the correct detection of the atomic positions. By contrast, the extra diffraction intensity due to slight substrate reconstructions, as for example buckling, seems to have negligible influence on the images. Due to the spatial information depth of the method the stacking of the cluster can be imaged down to the fourth layer. Finally, it is demonstrated how this structural knowledge of the adcluster geometry can be used to guide the dynamical intensity analysis subsequent to the holographic reconstruction and necessary to retrieve the full unit cell structure.Comment: 11 pages RevTex, 6 figures, Phys. Rev. B in pres

Tracking primary thermalization events in graphene with photoemission at extreme timescales

Direct and inverse Auger scattering are amongst the primary processes that mediate the thermalization of hot carriers in semiconductors. These two processes involve the annihilation or generation of an electron-hole pair by exchanging energy with a third carrier, which is either accelerated or decelerated. Inverse Auger scattering is generally suppressed, as the decelerated carriers must have excess energies higher than the band gap itself. In graphene, which is gapless, inverse Auger scattering is instead predicted to be dominant at the earliest time delays. Here, $<8$ femtosecond extreme-ultraviolet pulses are used to detect this imbalance, tracking both the number of excited electrons and their kinetic energy with time- and angle-resolved photoemission spectroscopy. Over a time window of approximately 25 fs after absorption of the pump pulse, we observe an increase in conduction band carrier density and a simultaneous decrease of the average carrier kinetic energy, revealing that relaxation is in fact dominated by inverse Auger scattering. Measurements of carrier scattering at extreme timescales by photoemission will serve as a guide to ultrafast control of electronic properties in solids for PetaHertz electronics.Comment: 16 pages, 8 figure

Prediction of huge X-ray Faraday rotation at the Gd N_4,5 threshold

X-ray absorption spectra in a wide energy range around the 4d-4f excitation threshold of Gd were recorded by total electron yield from in-plane magnetized Gd metal films. Matching the experimental spectra to tabulated absorption data reveals unprecedented short light absorption lengths down to 3 nm. The associated real parts of the refractive index for circularly polarized light propagating parallel or antiparallel to the Gd magnetization, determined through the Kramers-Kronig transformation, correspond to a magneto-optical Faraday rotation of 0.7 degrees per atomic layer. This finding shall allow the study of magnetic structure and magnetization dynamics of lanthanide elements in nanosize systems and dilute alloys.Comment: 4 pages, 2 figures, final version resubmitted to Phys. Rev. B, Brief Reports. Minor change