Semiclassical Analysis of a Detuned Ring Laser with a Saturable Absorber: New Results for the Steady States

This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately

Semiclassical Analysis of a Detuned Ring Laser with a Saturable Absorber: New Results for the Steady States

This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Quantifying the recent expansion of native invasive rush species in a UK upland environment

Rushes, such as soft rush (Juncus effusus L.), hard rush (Juncus inflexus L.) and compact rush (Juncus conglomeratus L.) have become problem species within upland grasslands across the UK and the coastal grasslands of western Norway. Indeed, being largely unpalatable to livestock and having a vigorous reproductive ecology means that they can rapidly come to dominate swards. However, rush dominance results in a reduction in grassland biodiversity and farm productivity. Anecdotal evidence from the UK suggests that rush cover within marginal upland grasslands has increased considerably in recent decades. Yet, there is currently no published evidence to support this observation. Here, we use recent and historical Google Earth imagery to measure changes in rush frequency over a 13-year period within four survey years: 2005, 2009, 2015 and 2018. During each survey year, we quantified rush presence or absence using a series of quadrats located within 300 upland grassland plots in the West Pennine Moors, UK. Data were analysed in two stages, first, by calculating mean rush frequencies per sample year using all the available plot-year combinations (the full dataset), and second by examining 25 differences in rush frequency using only the plots for which rush frequency data were available in every sample year (the continuous dataset). The full dataset indicated that rush frequency has increased by 82% between 2005 and 2018. Similarly, the continuous dataset suggested that rush frequency has increased by 174% over the same period, with the increases in frequency being statistically significant (P<0.05) between 2005-2018 and 2009-2018. We discuss the potential drivers of rush expansion in the West Pennine Moors, the ecological and agronomic implications of grassland rush infestations, and priorities for future research

MarcoPolo-R: Near-Earth Asteroid sample return mission selected for the assessment study phase of the ESA program cosmic vision

This paper presents the sample return mission to a primitive Near-Earth Asteroid (NEA) MarcoPolo-R proposed to the European Space Agency in December 2010. MarcoPolo-R was selected in February 2011 with three other missions addressing different science objectives for the two-year Assessment Phase of the Medium-Class mission competition of the Cosmic Vision 2 program for launch in 2022. The baseline target of MarcoPolo-R is the binary NEA (175706) 1996 FG3, which offers an efficient operational and technical mission profile. A binary target also provides enhanced science return. The choice of a binary target allows several scientific investigations to occur more easily than through a single object, in particular regarding the fascinating geology and geophysics of asteroids. MarcoPolo-R will rendezvous with a primitive, organic-rich NEA, scientifically characterize it at multiple scales, and return a bulk sample to Earth for laboratory analyses. The MarcoPolo-R sample will provide a representative sample from the surface of a known asteroid with known geologic context, and will contribute to the inventory of primitive material that is probably missing from the meteorite collection. The MarcoPolo-R samples will thus contribute to the exploration of the origin of planetary materials and initial stages of habitable planet formation, to the identification and characterization of the organics and volatiles in a primitive asteroid and to the understanding of the unique geomorphology, dynamics and evolution of a binary asteroid that belongs to the Potentially Hazardous Asteroid (PHA) population

Dusty Planetary Systems

Extensive photometric stellar surveys show that many main sequence stars show emission at infrared and longer wavelengths that is in excess of the stellar photosphere; this emission is thought to arise from circumstellar dust. The presence of dust disks is confirmed by spatially resolved imaging at infrared to millimeter wavelengths (tracing the dust thermal emission), and at optical to near infrared wavelengths (tracing the dust scattered light). Because the expected lifetime of these dust particles is much shorter than the age of the stars (>10 Myr), it is inferred that this solid material not primordial, i.e. the remaining from the placental cloud of gas and dust where the star was born, but instead is replenished by dust-producing planetesimals. These planetesimals are analogous to the asteroids, comets and Kuiper Belt objects (KBOs) in our Solar system that produce the interplanetary dust that gives rise to the zodiacal light (tracing the inner component of the Solar system debris disk). The presence of these "debris disks" around stars with a wide range of masses, luminosities, and metallicities, with and without binary companions, is evidence that planetesimal formation is a robust process that can take place under a wide range of conditions. This chapter is divided in two parts. Part I discusses how the study of the Solar system debris disk and the study of debris disks around other stars can help us learn about the formation, evolution and diversity of planetary systems by shedding light on the frequency and timing of planetesimal formation, the location and physical properties of the planetesimals, the presence of long-period planets, and the dynamical and collisional evolution of the system. Part II reviews the physical processes that affect dust particles in the gas-free environment of a debris disk and their effect on the dust particle size and spatial distribution.Comment: 68 pages, 25 figures. To be published in "Solar and Planetary Systems" (P. Kalas and L. French, Eds.), Volume 3 of the series "Planets, Stars and Stellar Systems" (T.D. Oswalt, Editor-in-chief), Springer 201

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Grain Surface Models and Data for Astrochemistry

AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions