Efficient long division via Montgomery multiply

We present a novel right-to-left long division algorithm based on the Montgomery modular multiply, consisting of separate highly efficient loops with simply carry structure for computing first the remainder (x mod q) and then the quotient floor(x/q). These loops are ideally suited for the case where x occupies many more machine words than the divide modulus q, and are strictly linear time in the "bitsize ratio" lg(x)/lg(q). For the paradigmatic performance test of multiword dividend and single 64-bit-word divisor, exploitation of the inherent data-parallelism of the algorithm effectively mitigates the long latency of hardware integer MUL operations, as a result of which we are able to achieve respective costs for remainder-only and full-DIV (remainder and quotient) of 6 and 12.5 cycles per dividend word on the Intel Core 2 implementation of the x86_64 architecture, in single-threaded execution mode. We further describe a simple "bit-doubling modular inversion" scheme, which allows the entire iterative computation of the mod-inverse required by the Montgomery multiply at arbitrarily large precision to be performed with cost less than that of a single Newtonian iteration performed at the full precision of the final result. We also show how the Montgomery-multiply-based powering can be efficiently used in Mersenne and Fermat-number trial factorization via direct computation of a modular inverse power of 2, without any need for explicit radix-mod scalings.Comment: 23 pages; 8 tables v2: Tweak formatting, pagecount -= 2. v3: Fix incorrect powers of R in formulae [7] and [11] v4: Add Eldridge & Walter ref. v5: Clarify relation between Algos A/A',D and Hensel-div; clarify true-quotient mechanics; Add Haswell timings, refs to Agner Fog timings pdf and GMP asm-timings ref-page. v6: Remove stray +bw in MULL line of Algo D listing; add note re byte-LUT for qinv_

Long's Vortex Revisited

The conical self-similar vortex solution of Long (1961) is reconsidered, with a view toward understanding what, if any, relationship exists between Long's solution and the more-recent similarity solutions of Mayer and Powell (1992), which are a rotational-flow analogue of the Falkner-Skan boundary-layer flows, describing a self-similar axisymmetric vortex embedded in an external stream whose axial velocity varies as a power law in the axial (z) coordinate, with phi=r/z^n being the radial similarity coordinate and n the core growth rate parameter. We show that, when certain ostensible differences in the formulations and radial scalings are properly accounted for, the Long and Mayer-Powell flows in fact satisfy the same system of coupled ordinary differential equations, subject to different kinds of outer-boundary conditions, and with Long's equations a special case corresponding to conical vortex core growth, n=1 with outer axial velocity field decelerating in a 1/z fashion, which implies a severe adverse pressure gradient. For pressure gradients this adverse Mayer and Powell were unable to find any leading-edge-type vortex flow solutions which satisfy a basic physicality criterion based on monotonicity of the total-pressure profile of the flow, and it is shown that Long's solutions also violate this criterion, in an extreme fashion. Despite their apparent nonphysicality, the fact that Long's solutions fit into a more general similarity framework means that nonconical analogues of these flows should exist. The far-field asymptotics of these generalized solutions are derived and used as the basis for a hybrid spectral-numerical solution of the generalized similarity equations, which reveal the existence of solutions for more modestly adverse pressure gradients than those in Long's case, and which do satisfy the above physicality criterion.Comment: 30 pages, including 16 figure

Acoustic transducer apparatus with reduced thermal conduction

A horn is described for transmitting sound from a transducer to a heated chamber containing an object which is levitated by acoustic energy while it is heated to a molten state, which minimizes heat transfer to thereby minimize heating of the transducer, minimize temperature variation in the chamber, and minimize loss of heat from the chamber. The forward portion of the horn, which is the portion closest to the chamber, has holes that reduce its cross-sectional area to minimize the conduction of heat along the length of the horn, with the entire front portion of the horn being rigid and having an even front face to efficiently transfer high frequency acoustic energy to fluid in the chamber. In one arrangement, the horn has numerous rows of holes extending perpendicular to the length of horn, with alternate rows extending perpendicular to one another to form a sinuous path for the conduction of heat along the length of the horn

Quick-MESS: A fast statistical tool for Exoplanet Imaging Surveys

Several tools have been developed in the past few years for the statistical analysis of the exoplanet search surveys, mostly using a combination of Monte-Carlo simulations or a Bayesian approach.Here we present the Quick-MESS, a grid-based, non-Monte Carlo tool aimed to perform statistical analyses on results from and help with the planning of direct imaging surveys. Quick-MESS uses the (expected) contrast curves for direct imaging surveys to assess for each target the probability that a planet of a given mass and semi-major axis can be detected. By using a grid-based approach Quick-MESS is typically more than an order of magnitude faster than tools based on Monte-Carlo sampling of the planet distribution. In addition, Quick-MESS is extremely flexible, enabling the study of a large range of parameter space for the mass and semi-major axes distributions without the need of re-simulating the planet distribution. In order to show examples of the capabilities of the Quick-MESS, we present the analysis of the Gemini Deep Planet Survey and the predictions for upcoming surveys with extreme-AO instruments.Comment: keywords: Stars, Extrasolar Planets, Data Analysis and Technique

Transport calculation of dilepton production at ultrarelativistic energies

Dilepton spectra are calculated within the microscopic transport model UrQMD and compared to data from the CERES experiment. The invariant mass spectra in the region 300 MeV < M < 600 MeV depend strongly on the mass dependence of the $\rho$ meson decay width which is not sufficiently determined by the Vector Meson Dominance model. A consistent explanation of both the recent Pb+Au data and the proton induced data can be given without additional medium effects

Self-diffusion in sheared colloidal suspensions: violation of fluctuation-dissipation relation

Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e. Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian Dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature

Time resolved spectroscopy of dust and gas from extrasolar planetesimals orbiting WD 1145+017

Multiple long and variable transits caused by dust from possibly disintegrating asteroids were detected in light curves of WD 1145+017. We present time-resolved spectroscopic observations of this target with QUCAM CCDs mounted in the Intermediate dispersion Spectrograph and Imaging System at the 4.2-m William Herschel Telescope in two different spectral arms: the blue arm covering 3800-4025 {\AA} and the red arm covering 7000-7430 {\AA}. When comparing individual transits in both arms, our observations show with 20 {\sigma} significance an evident colour difference between the in- and out-of-transit data of the order of 0.05-0.1 mag, where transits are deeper in the red arm. We also show with > 6 {\sigma} significance that spectral lines in the blue arm are shallower during transits than out-of-transit. For the circumstellar lines it also appears that during transits the reduction in absorption is larger on the red side of the spectral profiles. Our results confirm previous findings showing the u'-band excess and a decrease in line absorption during transits. Both can be explained by an opaque body blocking a fraction of the gas disc causing the absorption, implying that the absorbing gas is between the white dwarf and the transiting objects. Our results also demonstrate the capability of EMCCDs to perform high-quality time resolved spectroscopy of relatively faint targets.Comment: 9 pages, 5 figures. Accepted to MNRA

CAIR: Using Formal Languages to Study Routing, Leaking, and Interception in BGP

The Internet routing protocol BGP expresses topological reachability and policy-based decisions simultaneously in path vectors. A complete view on the Internet backbone routing is given by the collection of all valid routes, which is infeasible to obtain due to information hiding of BGP, the lack of omnipresent collection points, and data complexity. Commonly, graph-based data models are used to represent the Internet topology from a given set of BGP routing tables but fall short of explaining policy contexts. As a consequence, routing anomalies such as route leaks and interception attacks cannot be explained with graphs. In this paper, we use formal languages to represent the global routing system in a rigorous model. Our CAIR framework translates BGP announcements into a finite route language that allows for the incremental construction of minimal route automata. CAIR preserves route diversity, is highly efficient, and well-suited to monitor BGP path changes in real-time. We formally derive implementable search patterns for route leaks and interception attacks. In contrast to the state-of-the-art, we can detect these incidents. In practical experiments, we analyze public BGP data over the last seven years