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We report the generation of correlated photon pairs in the telecom C-band, at room temperature, from a dispersion-engineered silicon photonic crystal waveguide. The spontaneous four-wave mixing process producing the photon pairs is enhanced by slow-light propagation enabling an active device length of less than 100 {\mu}m. With a coincidence to accidental ratio of 12.8, at a pair generation rate of 0.006 per pulse, this ultra-compact photon pair source is immediately applicable towards scalable quantum information processing realized on-chip., Comment: 3 pages, 3 figures

We demonstrate photon-pair generation in a reverse proton exchanged waveguide fabricated on a periodically poled magnesium doped stoichiometric lithium tantalate substrate. Detected pairs are generated via a cascaded second order nonlinear process where a pump laser at wavelength of 1.55 $\mu$m is first doubled in frequency by second harmonic generation and subsequently downconverted around the same spectral region. Pairs are detected at a rate of 42 per second with a coincidence to accidental ratio of 0.7. This cascaded pair generation process is similar to four-wave-mixing where two pump photons annihilate and create a correlated photon pair.

We demonstrate the first 1550 nm correlated photon-pair source in an integrated glass platform-a chalcogenide As2S3 waveguide. A measured pair coincidence rate of 80 per second was achieved using 57 mW of continuous-wave pump. The coincidence to accidental ratio was shown to be limited by spontaneous Raman scattering effects that are expected to be mitigated by using a pulsed pump source., Comment: 3 pages, 4 figures

The multiplicities of stars, and some other properties, were collected recently by Eggleton & Tokovinin, for the set of 4559 stars with Hipparcos magnitude brighter than 6.0 (4558 excluding the Sun). In this paper I give a numerical recipe for constructing, by a Monte Carlo technique, a theoretical ensemble of multiple stars that resembles the observed sample. Only multiplicities up to 8 are allowed; the observed set contains only multiplicities up to 7. In addition, recipes are suggested for dealing with the selection effects and observational uncertainties that attend the determination of multiplicity. These recipes imply, for example, that to achieve the observed average multiplicity of 1.53, it would be necessary to suppose that the real population has an average multiplicity slightly over 2.0. This numerical model may be useful for (a) comparison with the results of star and star cluster formation theory, (b) population synthesis that does not ignore multiplicity above 2, and (c) initial conditions for dynamical cluster simulations.

Luminous X-ray stars are very often found in visual double or multiple stars. Binaries with periods of a few days possess the highest degree of coronal X-ray activity among regular, non-relativistic stars because of their fast, tidally driven rotation. But the orbital periods in visual double stars are too large for any direct interaction between the companions to take place. We suggest that most of the strongest X-ray components in resolved binaries are yet-undiscovered short-period binaries, and that a few are merged remnants of such binaries. The omnipresence of short-period active stars, e.g. of BY-Dra-type binaries, in multiple systems is explained via the dynamical evolution of triple stars with large mutual inclinations. The dynamical perturbation on the inner pair pumps up the eccentricity in a cyclic manner, a phenomenon known as Kozai cycling. At times of close periapsis, tidal friction reduces the angular momentum of the binary, causing it to shrink. When the orbital period of the inner pair drops to a few days, fast surface rotation of the companions is driven by tidal forces, boosting activity by a few orders of magnitude. If the period drops still further, a merger may take place leaving a rapidly-rotating active dwarf with only a distant companion.

Numerical simulations are used to study how fiber supercontinuum generation seeded by picosecond pulses can be actively controlled through the use of input pulse modulation. By carrying out multiple simulations in the presence of noise, we show how tailored supercontinuum Spectra with increased bandwidth and improved stability can be generated using an input envelope modulation of appropriate frequency and depth. The results are discussed in terms of the non-linear propagation dynamics and pump depletion., Comment: Aspects of this work were presented in Paper ThJ2 at OECC/ACOFT 2008, Sydney Australia 7-10 July (2008). Journal paper submitted for publication 30 July 2008

We consider the multiplicity of stellar systems with (combined) magnitude brighter than 6.00 in Hipparcos magnitudes. We identify 4559 such bright systems (including the Sun), and the frequencies of multiplicities 1, 2,..., 7 are found to be 2718, 1437, 285, 86, 20, 11 and 2. We discuss the uncertainties, which are substantial. We also consider the distributions of periods of orbits and sub-orbits. We note that for the even more restricted set of 478 systems with V_H <= 4.00 the proportions of higher multiples up to sextuple are progressively larger (213, 179, 54, 19, 8, 5), suggesting substantial incompleteness in even the reasonably well-studied larger sample. This sample can be seen as relatively thoroughly studied for multiplicity, and reasonably representative of stars more massive than the Sun. But the restriction to V_H <= 6 means that our sample contains hardly any systems where all components are low-mass main-sequence stars (K or M). Data on multiplicity is important as a constraint on (a) the star-formation problem, (b) the problem of the evolution of the Galactic stellar population, and (c) the interaction of dynamics and evolution through the effect of Kozai cycles. We discuss these topics briefly., Comment: Accepted for publication in MNRAS 11 pages, 1 figure, 3 tables: http://www.ctio.noao.edu/ftp/pub/tokovinin/eggleton2008/Table1.txt http://www.ctio.noao.edu/ftp/pub/tokovinin/eggleton2008/Table2.txt http://www.ctio.noao.edu/ftp/pub/tokovinin/eggleton2008/Table1.txt

We present a numerical study of the evolution dynamics of ``optical rogue waves'', statistically-rare extreme red-shifted soliton pulses arising from supercontinuum generation in photonic crystal fiber [D. R. Solli et al. Nature Vol. 450, 1054-1058 (2007)]. Our specific aim is to use nonlinear Schrodinger equation simulations to identify ways in which the rogue wave dynamics can be actively controlled, and we demonstrate that rogue wave generation can be enhanced by an order of magnitude through a small modulation across the input pulse envelope and effectively suppressed through the use of a sliding frequency filter., Comment: Submitted for Publication (2008)

We demonstrate a method to locally change the refractive index in planar optical devices by photodarkening of a thin chalcogenide glass layer deposited on top of the device. The method is used to tune the resonance of GaAs-based photonic crystal cavities by up to 3 nm at 940 nm, with only 5% deterioration in cavity quality factor. The method has broad applications for postproduction tuning of photonic devices., Comment: 3 pages, 2 figures

Three-dimensional stellar modeling has enabled us to identify a deep-mixing mechanism that must operate in all low mass giants. This mixing process is not optional, and is driven by a molecular weight inversion created by the 3He(3He,2p)4He reaction. In this paper we characterize the behavior of this mixing, and study its impact on the envelope abundances. It not only eliminates the problem of 3He overproduction, reconciling stellar and big bang nucleosynthesis with observations, but solves the discrepancy between observed and calculated CNO isotope ratios in low mass giants, a problem of more than 3 decades' standing. This mixing mechanism, which we call `$\delta\mu$-mixing', operates rapidly (relative to the nuclear timescale of overall evolution, ~ 10^8 yrs) once the hydrogen burning shell approaches the material homogenized by the surface convection zone. In agreement with observations, Pop I stars between 0.8 and 2.0$\Msun$ develop 12C/13C ratios of 14.5 +/- 1.5, while Pop II stars process the carbon to ratios of 4.0 +/- 0.5. In stars less than 1.25$\Msun$, this mechanism also destroys 90% to 95% of the 3He produced on the main sequence., Comment: Final accepted version (submitted to Astrophys J in Jan 2007...)

We continue our study of the core helium flash using the three dimensional hydrodynamics code Djehuty. Continuing from earlier calculations, we now take relaxed 3D configurations and add various amounts of rotation. We find that rotation periods consistent with those observed in white dwarfs produce negligible changes in the structure and evolution of the core flash, at least for the very small timescales we have yet been able to investigate. There is no sign of any extra mixing due to the rotation. There is some inconclusive evidence for a slight change in the luminosity, at the 1% level., Comment: Accepted for publication in the (refereed) Proceedings of the Nuclei In The Cosmos IX meeting

Low-mass stars, ~1-2 solar masses, near the Main Sequence are efficient at producing 3He, which they mix into the convective envelope on the giant branch and distribute into the Galaxy by way of envelope loss. This process is so efficient that it is difficult to reconcile the observed cosmic abundance of 3He with the predictions of Big Bang nucleosynthesis. In this paper we find, by modeling a red giant with a fully three-dimensional hydrodynamic code and a full nucleosynthetic network, that mixing arises in the supposedly stable and radiative zone between the hydrogen-burning shell and the base of the convective envelope. This mixing is due to Rayleigh-Taylor instability within a zone just above the hydrogen-burning shell. In this zone the burning of the 3He left behind by the retreating convective envelope is predominantly by the reaction 3He + 3He -> 4He + 2p, a reaction which, untypically for stellar nuclear reactions, {\it lowers} the mean molecular weight, leading to a local minimum. This local minimum leads to Rayleigh-Taylor instability, and turbulent motion is generated which will continue ultimately up into the normal convective envelope. Consequently material from the envelope is dragged down sufficiently close to the burning shell that the 3He in it is progressively destroyed. Thus we are able to remove the threat that 3He production in low-mass stars poses to the Big Bang nucleosynthesis of 3He. Some slow mixing mechanism has long been suspected, that connects the convective envelope of a red giant to the burning shell. It appears to be necessary to account for progressive changes in the 12C/13C and 14N/12C ratios on the First Giant Branch. We suggest that these phenomena are also due to the Rayleigh-Taylor-unstable character of the 3He-burning region., Comment: Paper presented at IAU-GA, Prague, August 2006

Low-mass stars, ~1-2 solar masses, near the Main Sequence are efficient at producing He-3, which they mix into the convective envelope on the giant branch and should distribute into the Galaxy by way of envelope loss. This process is so efficient that it is difficult to reconcile the low observed cosmic abundance of He-3 with the predictions of both stellar and Big Bang nucleosynthesis. In this paper we find, by modeling a red giant with a fully three-dimensional hydrodynamic code and a full nucleosynthetic network, that mixing arises in the supposedly stable and radiative zone between the hydrogen-burning shell and the base of the convective envelope. This mixing is due to Rayleigh-Taylor instability within a zone just above the hydrogen-burning shell, where a nuclear reaction lowers the mean molecular weight slightly. Thus we are able to remove the threat that He-3 production in low-mass stars poses to the Big Bang nucleosynthesis of He-3., Comment: Accepted by Science, and available from Science Express online

We model the core helium flash in a low-mass red giant using Djehuty, a fully three-dimensional (3D) code. The 3D structures were generated from converged models obtained during the 1D evolutionary calculation of a 1$\Msun$ star. Independently of which starting point we adopted, we found that after some transient relaxation the 3D model settled down with a briskly convecting He-burning shell that was not very different from what the 1D model predicted., Comment: 32 pages, 13 figures, accepted by ApJ. Figures reduced from high-res eps to low-res gif for rapid download. Contact Lattanzio for a copy of the higher res images (included, inplace, in the manuscript)

We study the dynamical interaction in which the two single runaway stars AE Aurigae and mu Columbae and the binary iota Orionis acquired their unusually high space velocity. The two single runaways move in almost opposite directions with a velocity greater than 100 km/s away from the Trapezium cluster. The star iota Ori is an eccentric (e=0.8) binary moving with a velocity of about 10 km/s at almost right angles with respect to the two single stars. The kinematic properties of the system suggest that a strong dynamical encounter occurred in the Trapezium cluster about 2.5 Myr ago. Curiously enough, the two binary components have similar spectral type but very different masses, indicating that their ages must be quite different. This observation leads to the hypothesis that an exchange interaction occurred in which an older star was swapped into the original iota Orionis binary. We test this hypothesis by a combination of numerical and theoretical techniques, using N-body simulations to constrain the dynamical encounter, binary evolution calculations to constrain the high orbital eccentricity of iota Orionis and stellar evolution calculations to constrain the age discrepancy of the two binary components. We find that an encounter between two low eccentricity (0.4

Current practice in stellar evolution is to employ one-dimensional calculations that quantitatively apply only to a minority of the observed stars (single non-rotating stars, or well detached binaries). Even in these systems, astrophysicists are dependent on approximations to handle complex three-dimensional processes like convection. Understanding the structure of binary stars, like those that lead to the Type Ia supernovae used to measure the expansion of the universe, are grossly non-spherical and await a 3D treatment. To approach very large problems like multi-dimensional modeling of stars, the Lawrence Livermore National Laboratory has invested in massively parallel computers and invested even more in developing the algorithms to utilize them on complex physics problems. We have leveraged skills from across the lab to develop a 3D stellar evolution code, Djehuty (after the Egyptian god for writing and calculation) that operates efficiently on platforms with thousands of nodes, with the best available physical data (opacities, EOS, etc.). Djehuty has incorporated all basic physics for modeling stars including an accurate equation of state, radiation transport by diffusion, thermonuclear reaction rates, and hydrodynamics, and we have begun testing it in a number of applications., Comment: 14 pages, 8 figures. Proceedings of the 3D Stellar Evolution workshop held in Livermore, July 22-26 2002. ASP Conf. Series vol. 293

The orbits in the HD 160691 planetary system at first appeared highly unstable, but using the MEGNO and FLI techniques of global dynamics analysis in the orbital parameter space we have found a stabilizing mechanism that could be the key to its existence. In order to be dynamically stable, the HD 160691 planetary system has to satisfy the following conditions: (1) a 2:1 mean motion resonance, combined with (2) an apsidal secular resonance in (3) a configuration $P_{c}(ap) - S - P_{b}(ap)$ where the two apsidal lines are anti-aligned, and (4) specific conditions on the respective sizes of the eccentricities (high eccentricity for the outer orbit is in particular the most probable necessary condition). More generally, in this original orbital topology, where the resonance variables $\theta_{1}$ and $\theta_{3}$ librate about $180^{\circ}$ while $\theta_{2}$ librates about $0^{\circ}$, the HD 160691 system and its mechanism have revealed aspects of the 2:1 orbital resonances that have not been observed nor analyzed before. The present topology combined with the 2:1 resonance is indeed more wide-ranging than the particular case of the HD 160691 planetary system. It is a new theoretical possibility suitable for a stable regime despite relatively small semi-major axes with respect to the important masses in interactions., Comment: 21 pages, 8 figures, 1 table, accepted version to ApJ (31 Jul 2003)

This is a summary paper of MODEST-2, a workshop held at the Astronomical Institute ``Anton Pannekoek'' in Amsterdam, 16-17 December 2002. MODEST is a loose collaboration of people interested in MOdelling DEnse STellar systems, particularly those interested in modelling these systems using all the available physics (stellar dynamics, stellar evolution, hydrodynamics and the interplay between the three) by defining interfaces between different codes. In this paper, we summarize 1) the main advances in this endeavour since MODEST-1; 2) the main science goals which can be and should be addressed by these types of simulations; and 3) the most pressing theoretical and modelling advances that we identified., Comment: Accepted by New Astronomy

We discuss the evolution of binaries with moderately high masses (about 10 - 30 solar masses), and with periods of about 3 - 300d, corresponding mostly to early Case B. These are usually thought to evolve either by reasonably conservative Roche-lobe overflow, if the initial mass ratio is fairly mild, or else by highly non-conservative common-envelope evolution, with spiral-in to short periods (hours, typically), if the initial mass ratio is rather extreme. We discuss here a handful of binaries from part of this period range (about 50 - 250d), which appear to have followed a different path: we argue that they must have lost a large proportion of initial mass (about 70 - 80%), but without shortening their periods at all. We suggest that their behaviour may be due to the fact that stars of such masses, when evolved also to rather large radii, are not far from the Humphreys-Davidson limit where single stars lose their envelopes spontaneously in P Cygni winds, and so have envelopes which are only lightly bound to the core. These envelopes therefore may be relatively easily dissipated by the perturbing effect of a companion. In addition, some or all of the stars considered here may have been close to the Cepheid instability strip when they filled their Roche lobes. One or other, or both, of high luminosity and Cepheid instability, in combination with an appropriately close binary companion, may be implicated.

In order to distinguish between regular and chaotic planetary orbits we apply a new technique called MEGNO in a wide neighbourhood of orbital parameters determined using standard two-body Keplerian fits for HD 12661, HD 38529, HD 37124 and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system., Comment: 12 pages, 3 figures, accepted ApJ, revised version following the referee's report

As mathematics teacher education promotes the mathematics and pedagogical practices of the National Council of Teachers of Mathematics (NCTM) Standards, most mathematics preservice teachers confront philosophies of mathematics significantly different from their personal mathematical philosophy. The constructivist/quasi-empiricist mathematical philosophy espoused by the NCTM "Standards," as opposed to the traditional absolutist philosophy of mathematics as a set of rules and facts, characterizes the conflict in philosophies of mathematics. This report shares the findings from an in-depth case study of a preservice secondary mathematics teacher, Ken, by following the subtle evolution of his philosophy of mathematics, as characterized by Ernest's "Mathematics-Related Belief Systems," and the experiences influential in his philosophical evolution over a year of preservice mathematics teacher education. Contains 12 references. (Author)

The DJEHUTY project is an intensive effort at the Lawrence Livermore National Laboratory (LLNL) to produce a general purpose 3-D stellar structure and evolution code to study dynamic processes in whole stars., Comment: 2 pages, IAU coll. 185

We consider dynamical effects of additional perturbative forces due to the non-point mass nature of stars and planets: effects such as quadrupolar distortion and tidal friction in the systems of exo-planets. It is shown that these forces should not be neglected while modelling the dynamics of planetary systems, especially taking into account the undefined real masses of the planets due to unknown orbital inclinations and the unsatisfactory application of Keplerian fits to the radial velocity data in multiple planetary systems., Comment: 5 pages, 2 figures, accepted by ApJ Let

Using Eggleton's stellar evolution code, we carry out 150 runs of Pop I binary evolution calculations, with the initial primary mass between 1 and 8 solar masses the initial mass ratio between 1.1 and 4, and the onset of Roche lobe overflow (RLOF) at an early, middle, or late Hertzsprung-gap stage. We assume that RLOF is conservative in the calculations, and find that the remnant mass of the primary may change by more than 40 per cent over the range of initial mass ratio or orbital period, for a given primary mass. This is contrary to the often-held belief that the remnant mass depends only on the progenitor mass if mass transfer begins in the Hertzsprung gap. We fit a formula, with an error less than 3.6 per cent, for the remnant (white dwarf) mass as a function of the initial mass of the primary, the initial mass ratio, and the radius of the primary at the onset of RLOF. We also find that a carbon-oxygen white dwarf with mass as low as 0.33 solar masses may be formed if the primary's initial mass is around 2.5 solar masses., Comment: 7 pages for main text, 11 pages for appendix (table A1), 12 figures

We undertake a comparison of observed Algol-type binaries with a library of computed Case A binary evolution tracks. The library consists of 5500 binary tracks with various values of initial primary mass M_{10}, mass ratio q_0, and period P_0, designed to sample the phase-space of Case A binaries in the range -0.10 < log M_{10} < 1.7. Each binary is evolved using a standard code with the assumption that both total mass and orbital angular momentum are conserved. This code follows the evolution of both stars until the point where contact or reverse mass transfer occurs. The resulting binary tracks show a rich variety of behavior which we sort into several subclasses of Case A and Case B. We present the results of this classification, the final mass ratio and the fraction of time spent in Roche Lobe overflow for each binary system. The conservative assumption under which we created this library is expected to hold for a broad range of binaries, where both components have spectra in the range G0 to B1 and luminosity class III - V. We gather a list of relatively well-determined observed hot Algol-type binaries meeting this criterion, as well as a list of cooler Algol-type binaries where we expect significant dynamo-driven mass loss and angular momentum loss. We fit each observed binary to our library of tracks using a chi^2-minimizing procedure. We find that the hot Algols display overall acceptable chi^2, confirming the conservative assumption, while the cool Algols show much less acceptable chi^2 suggesting the need for more free parameters, such as mass and angular momentum loss., Comment: Submitted to ApJ, 3 tables, 12 figures

We derive from first principles equations governing (a) the quadrupole tensor of a star distorted by both rotation and the presence of a companion in a possibly eccentric orbit, (b) a functional form for the dissipative force of tidal friction, based on the concept that the rate of energy loss from a time-dependent tide should be a positive-definite function of the rate of change of the quadrupole tensor as seen in the frame which rotates with the star, and (c) the equations governing the rates of change of the magnitude and direction of the stellar rotation, and the orbital period and eccentricity, based on the concept of the Laplace-Runge-Lenz vector. Our analysis leads relatively simply to a closed set of equations, valid for arbitrary inclination of the stellar spin to the orbit. The results are equivalent to classical results based on the rather less clear principle that the tidal bulge lags behind the line of centres by some time determined by the rate of dissipation; our analysis gives the effective lag time as a function of the dissipation rate and the quadrupole moment. We discuss briefly some possible applications of the formulation., Comment: LaTeX, 1 postscript figure included, ApJ, accepted

In this paper we study the formation, evolution and disruption of hierarchical systems in open clusters. With this purpose, N-body simulations of star clusters containing an initial population of binaries have been carried out using Aarseth's NBODY4 and NBODY5 codes. Stable triples may form from strong interactions of two binaries in which the widest pair is disrupted. The most frequent type of hierarchical systems found in the cluster models are triples in which the outer star is single, but in some cases the outer body is also a binary, giving a hierarchical quadruple. Many triple systems are non-coplanar and the presence of even a very distant and small outer companion may affect the orbital parameters of the inner binary, including a possible mechanism of significant shrinkage if the binary experiences a weak tidal dissipation. The main features of these systems are analyzed in order to derive general properties which can be checked by observations. The formation of exotic objects, such as blue stragglers and white dwarf binaries, inside hierarchical triple systems is particularly interesting., Comment: 14 pages, LaTeX, 6 ps figures. To be published in: Visual Double Stars: Formation, Dynamics and Evolutionary Tracks, eds. J. A. Docobo, A. Elipe, and H. McAlister, (KAP:ASSL Series)

About 5-15% of stellar systems are at least triple. About 1% of systems with a primary of $\tgs 1 \Mscun$ are triple with a {\it longer} peri od that is less than 30y, and so may in principle be capable of Roche-lobe overflow in both the inner and the outer orbits, at different times. We discuss possible evolutionary paths for these systems, some of which may lead to objects that are difficult to understand in the context of purely binary evolution. An example is OW Gem, a binary containing two supergiants (spectral types F and G) with masses that difffer by a factor of 1.5. There is also a triple-star pathway which could lead rather naturally to low-mass X-ray binaries; whereas binary pathways often appear rather contrived. We also discuss some dynamical pr ocesses involved in the 3-body problem. A number of triple stars are found in clusters. Similar systems can be created by gravitational capture during N-body simulations of Galactic clusters, especially if there is a n assumed primordial binary population. We discuss the properties of these triples , and note that many can be quite long-lived., Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.html

We present a simple and efficient, yet reasonably accurate, equation of state, which at the moderately low temperatures and high densities found in the interiors of stars less massive than the Sun is substantially more accurate than its predecessor by Eggleton, Faulkner & Flannery. Along with the most recently available values in tabular form of opacities, neutrino loss rates, and nuclear reaction rates for a selection of the most important reactions, this provides a convenient package of input physics for stellar modelling. We briefly discuss a few results obtained with the updated stellar evolution code., Comment: uuencoded compressed postscript. The preprint are also available at http://www.ast.cam.ac.uk/preprint/PrePrint.html