Large Range Of Initial Conditions Research Articles

Updated studies on exomoons in the HD 23079 system

Abstract We re-evaluate the outer edge of orbital stability for possible exomoons orbiting the radial velocity planet discovered in the HD 23079 system. In this system, a solar-type star hosts a Jupiter-mass planet in a nearly circular orbit in the outer stellar habitable zone. The outer stability limit of exomoons is deduced using N-body and tidal migration simulations considering a large range of initial conditions, encompassing both prograde and retrograde orbits. In particular, we extend previous works by evaluating many values in the satellite mean anomaly to identify and exclude regions of quasi-stability. Future observations of this system can make use of our results through a scale factor relative to the currently measured minimum mass. Using a constant time lag tidal model (Hut 1981), we find that plausible tidal interactions within the system are insufficient to induce significant outward migration toward the theoretical stability limit. While current technologies are incapable of detecting exomoons in this system, we comment on the detectability of putative moons through Doppler monitoring within direct imaging observations in view of future research capacities.

Contribution of viscosity to the circulation deposition in the Richtmyer–Meshkov instability

This study focuses on the process of the circulation deposition in the Richtmyer–Meshkov instability (RMI). The growth rate of circulation and its sources are theoretically and numerically studied to reveal the physical mechanism of the viscosity in the circulation deposition process. We derive a predicting model of the circulation rate for RMI. More importantly, all the contributing sources are separately predicted. Particularly, the viscous source, which previously lacked theoretical or numerical investigations, is efficiently predicted. The RMI problems in a large range of initial conditions are simulated with the direct simulation Monte Carlo (DSMC) method to verify our predicting model and further reveal the circulation deposition mechanism. The DSMC simulations provide reliable quantification of the circulation deposition (especially viscous contribution) for RMI due to its molecular nature. Our model predicts the circulation rate, baroclinic and viscous sources accurately for all the cases in comparison with the simulations. A new physical insight into the mechanism of viscosity in RMI is provided. Unlike the previous understandings that nearly all circulation deposition in RMI comes from the baroclinic source, this study reveals the hidden positive contribution of the viscous source, especially for high Mach number conditions (up to 11 % of total circulation rate). For RMI, the large viscosity gradient inside the shock waves plays a crucial role in the circulation deposition even under high Reynolds number conditions. Our study also provides exciting opportunities to further understand the viscous contribution to the vorticity dynamics in the reshocked RMI and shock wave–turbulence interactions.

Bayesian evidence for α-attractor dark energy models

Dark energy models with tracker properties have gained attention due to the large range of initial conditions leading to the current value of the dark energy density parameter. A well-motivated family of these models are the so-called α-attractors, which show the late time behavior of a cosmological constant. In the present paper we perform a model-selection analysis of a variety of α-attractor potentials in comparison with a non-flat ΛCDM model. Specifically, we compute the Bayes Factor for the L-Model, the Oscillatory Tracker Model, the Recliner Model, and the Starobinsky Model, while considering the non-flat ΛCDM as the base model. Each model is tested through a Bayesian analysis using observations relevant to the current accelerated expansion: we employ the latest SNe Ia data, combined with cosmic clocks, the latest BOSS release of BAO data, and the Planck Compressed 2018 data. The produced Markov Chains for each model are further compared through a Bayesian evidence analysis. From the latter we conclude that the Oscillatory Tracker Model is preferred by data (even if weakly) over the non-flat ΛCDM model. Our results also suggest at the L-model is the least favoured version of the α-attractor models considered.

Infalling Young Clusters in the Galactic Centre: implications for IMBHs and young stellar populations

The central parsec of the Milky Way hosts two puzzlingly young stellar populations, a tight isotropic distribution of B stars around SgrA* (the S-stars) and a disk of OB stars extending to ~0.5pc. Using a modified version of Sverre Aarseth's direct summation code NBODY6 we explore the scenario in which a young star cluster migrates to the Galactic Centre within the lifetime of the OB disk population via dynamical friction. We find that star clusters massive and dense enough to reach the central parsec form a very massive star via physical collisions on a mass segregation timescale. We follow the evolution of the merger product using the most up to date, yet conservative, mass loss recipes for very massive stars. Over a large range of initial conditions, we find that the very massive star expels most of its mass via a strong stellar wind, eventually collapsing to form a black hole of mass 20 - 400 M_Sun, incapable of bringing massive stars to the Galactic Centre. No massive intermediate mass black hole can form in this scenario. The presence of a star cluster in the central ~10 pc within the last 15 Myr would also leave a ~2 pc ring of massive stars, which is not currently observed. Thus, we conclude that the star cluster migration model is highly unlikely to be the origin of either young population, and in-situ formation models or binary disruptions are favoured.

Evaporation-Induced Pattern Formation of Decanol Droplets.

Pattern formation in far-from-equilibrium systems is observed in several disciplines including biology, geophysics, and reaction-diffusion chemistry, comprising both living and nonliving systems. We aim to study such nonequilibrium dynamics on the laboratory scale with materials of simple composition. We present a novel system based on a 1-decanol droplet placed in a solution of alkaline decanoate. Previously, we showed the short time scale behavior of this system, which included chemotaxis and maze solving. Here we explore long time scale dynamics of the system (several hours) when open to the environment. We observe dramatic morphological changes in the droplet including long tentacular structures, and we analyze the morphology of these structures at both the macroscopic and microscopic scales across a large range of initial conditions. Such reproducible morphological changes in simple droplets open a path to the exploration of shape-based effects in larger-scale pattern-formation studies.

Double-averaging can fail to characterize the long-term evolution of Lidov–Kozai Cycles and derivation of an analytical correction

The double-averaging (DA) approximation is widely employed as the standard technique in studying the secular evolution of the hierarchical three-body system. We show that effects stemmed from the short-timescale oscillations ignored by DA can accumulate over long timescales and lead to significant errors in the long-term evolution of the Lidov-Kozai cycles. In particular, the conditions for having an orbital flip, where the inner orbit switches between prograde and retrograde with respect to the outer orbit and the associated extremely high eccentricities during the switch, can be modified significantly. The failure of DA can arise for a relatively strong perturber where the mass of the tertiary is considerable compared to the total mass of the inner binary. This issue can be relevant for astrophysical systems such as stellar triples, planets in stellar binaries, stellar-mass binaries orbiting massive black holes and moons of the planets perturbed by the Sun. We derive analytical equations for the short-term oscillations of the inner orbit to the leading order for all inclinations, eccentricities and mass ratios. Under the test particle approximation, we derive the "corrected double-averaging" (CDA) equations by incorporating the effects of short-term oscillations into the DA. By comparing to N-body integrations, we show that the CDA equations successfully correct most of the errors of the long-term evolution under the DA approximation for a large range of initial conditions. We provide an implementation of CDA that can be directly added to codes employing DA equations.

Robust post-stall perching with a simple fixed-wing glider using LQR-Trees

Birds routinely execute post-stall maneuvers with a speed and precision far beyond the capabilities of our best aircraft control systems. One remarkable example is a bird exploiting post-stall pressure drag in order to rapidly decelerate to land on a perch. Stall is typically associated with a loss of control authority, and it is tempting to attribute this agility of birds to the intricate morphology of the wings and tail, to their precision sensing apparatus, or their ability to perform thrust vectoring. Here we ask whether an extremely simple fixed-wing glider (no propeller) with only a single actuator in the tail is capable of landing precisely on a perch from a large range of initial conditions. To answer this question, we focus on the design of the flight control system; building upon previous work which used linear feedback control design based on quadratic regulators (LQR), we develop nonlinear feedback control based on nonlinear model-predictive control and ‘LQR-Trees’. Through simulation using a flat-plate model of the glider, we find that both nonlinear methods are capable of achieving an accurate bird-like perching maneuver from a large range of initial conditions; the ‘LQR-Trees’ algorithm is particularly useful due to its low computational burden at runtime and its inherent performance guarantees. With this in mind, we then implement the ‘LQR-Trees’ algorithm on real hardware and demonstrate a 95 percent perching success rate over 147 flights for a wide range of initial speeds. These results suggest that, at least in the absence of significant disturbances like wind gusts, complex wing morphology and sensing are not strictly required to achieve accurate and robust perching even in the post-stall flow regime.

Showing or telling? Local interaction and organization of behavior

We present a choice model based on agent interaction. Interaction is modeled as face-to-face communication that takes place on a regular periodic lattice with decision-makers exchanging information only with immediate neighbors. We investigate the long-run (equilibrium) behavior of the resulting system and show that for a large range of initial conditions clustering in economic behavior emerges and persists indefinitely. Unlike many models in the literature, our model allows for the analysis of multi-option environments. Therefore, we add to existing results by deriving the equilibrium distribution of option popularity and thus, implicitly, of market shares. Additionally, the model sheds new light on the emergence of the novel behavior in societies.

COHESION, CONSENSUS AND EXTREME INFORMATION IN OPINION DYNAMICS

Opinion formation is an important element of social dynamics. It has been widely studied in the last years with tools from physics, mathematics and computer science. Here, a continuous model of opinion dynamics for multiple possible choices is analyzed. Its main features are the inclusion of disagreement and possibility of modulating external information/media effects, both from one and multiple sources. The interest is in identifying the effect of the initial cohesion of the population, the interplay between cohesion and media extremism, and the effect of using multiple external sources of information that can influence the system. Final consensus, especially with the external message, depends highly on these factors, as numerical simulations show. When no external input is present, consensus or segregation is determined by the initial cohesion of the population. Interestingly, when only one external source of information is present, consensus can be obtained, in general, only when this is extremely neutral, i.e., there is not a single opinion strongly promoted, or in the special case of a large initial cohesion and low exposure to the external message. On the contrary, when multiple external sources are allowed, consensus can emerge with one of them even when this is not extremely neutral, i.e., it carries a strong message, for a large range of initial conditions.

Creating sharp features by colliding shocks on uniformly irradiated surfaces

Using a theoretical analysis of the ion beam sputtering dynamics, we demonstrate how ion bombardment on an initially sloped surface can create knife-edge-like ridges on the surface. These ridges arise as nonclassical shocklike solutions that are undercompressive on both sides and appear to control the dynamics over a large range of initial conditions. The slope of the ridges is selected uniquely by the dynamics and can be up to 30 or more depending on the orientation dependence of the sputtering yield. For 1 keV Ar${}^{+}$ on Si(001), the scale of the ridge is $\ensuremath{\approx}\phantom{\rule{-0.16em}{0ex}}2$ nm. This is much smaller than the most unstable length scale and suggests a method for creating very steep, very sharp features on a surface spontaneously, by prepatterning the surface to contain relatively modest slopes on the macroscale.

The interplay of chaos between the terrestrial and giant planets

We report on some simple experiments on the nature of chaos in our planetary system. We make the following interesting observations. First, we look at the system of Sun + four Jovian planets as an isolated five-body system interacting only via Newtonian gravity. We find that if we measure the Lyapunov time of this system across thousands of initial conditions all within observational uncertainty, then the value of the Lyapunov time seems relatively smooth across some regions of initial condition space, while in other regions it fluctuates wildly on scales as small as we can reliably measure using numerical methods. This probably indicates a fractal structure of Lyapunov exponents measured across initial condition space. Then, we add the four inner terrestrial planets and several post-Newtonian corrections such as general relativity into the model. In this more realistic Sun + eight-planet system, we find that the above structure of chaos for the outer planets becomes uniformly chaotic for almost all planets and almost all initial conditions, with a Lyapunov time-scale of about 5–20 Myr. This seems to indicate that the addition of the inner planets adds more chaos to the system. Finally, we show that if we instead remove the outer planets and look at the isolated five-body system of the Sun + four terrestrial planets, then the terrestrial planets alone show no evidence of chaos at all, over a large range of initial conditions inside the observational error volume. We thus conclude that the uniformity of chaos in the outer planets comes not from the inner planets themselves, but from the interplay between the outer and inner ones. Interestingly, however, there exist rare and isolated initial conditions for which one individual outer planetary orbit may appear integrable over a 200-Myr time-scale, while all the other planets simultaneously appear chaotic.

ON THE EVOLUTION OF ANOMALOUS X-RAY PULSARS AND SOFT GAMMA-RAY REPEATERS WITH FALL BACK DISKS

We show that the period clustering of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs), their X-ray luminosities, ages, and statistics can be explained with fall back disks with large initial specific angular momentum. The disk evolution models are developed by comparison to self-similar analytical models. The initial disk mass and angular momentum set the viscous timescale. An efficient torque, with (1 − ω2*) dependence on the fastness parameter ω*, leads to period clustering in the observed AXP–SGR period range under a wide range of initial conditions. The timescale t0 for the early evolution of the fall back disk, and the final stages of fall back disk evolution, when the disk becomes passive, are the crucial determinants of the evolution. The disk becomes passive at temperatures around 100 K, which provides a natural cutoff for the X-ray luminosity and defines the end of evolution in the observable AXP and SGR phase. This low value for the minimum temperature for active disk turbulence indicates that the fall back disks are active up to a large radius, ≳1012 cm. We find that transient AXPs and SGRs are likely to be older than their persistent cousins. A fall back disk with mass transfer rates corresponding to the low quiescent X-ray luminosities of the transient sources in early evolutionary phases would have a relatively lower initial mass, such that the mass-flow rate in the disk is not sufficient for the inner disk to penetrate into the light cylinder of the young neutron star, making mass accretion onto the neutron star impossible. The transient AXP phase therefore must start later. The model results imply that the transient AXP/SGRs, although older, are likely to be similar in number to persistent sources. This is because the X-ray luminosities of AXPs and SGRs are found to decrease faster at the end of their evolution, and the X-ray luminosities of transient AXP and SGRs in quiescence lie in the luminosity range of X-ray cutoff phase. Taking the range of quiescent X-ray luminosities of transient AXPs and SGRs ∼1033–1034 erg s−1, our simulations imply that the duration of the cutoff phase is comparable to the lifetime in the persistent phase for a large range of initial conditions.

Ceres’ evolution and present state constrained by shape data

We model Ceres’ thermo-physical-chemical evolution by considering a large range of initial conditions as well as various evolutionary scenarios. Models are constrained by available shape measurements, which point to a differentiated interior for Ceres. We address the role played by hydrothermal activity in the long-term evolution of Ceres and especially the evolution of its hydrosphere. We suggest that models with times of formation shorter than about 5 My after the production of calcium–aluminum inclusions are more likely to undergo hydrothermal activity in their early history, which affects Ceres’ long-term thermal evolution. We evaluate the conditions for preserving liquid water inside Ceres, a possibility enhanced by its warm surface temperature and the enrichment of its hydrosphere in a variety of chemical species. However, thermal modeling of the hydrosphere needs to be further investigated. We show that shape data can help constrain the amount of hydrated silicate in the core, and thus the extent of hydrothermal activity in Ceres. We discuss the importance of these results for the Dawn mission’s arrival at Ceres in 2015.

Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation

Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-$x$ data in both the saturation region and the so-called extended geometric scaling (EGS) region. We investigate to what extent such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in $x$ of the dipole cross section in these momentum regions. We find that in the EGS region the BK equation yields results that are qualitatively different from those of phenomenological studies. In particular, geometric scaling around the saturation scale is only obtained at asymptotic rapidities. We find that in this limit the anomalous dimension $\ensuremath{\gamma}(r,x)$ of phenomenological models approaches a limiting function that is universal for a large range of initial conditions. At the saturation scale, this function equals approximately 0.44, in contrast to the value 0.628 commonly used in the models. We further investigate the dependence of these results on the starting distribution, the small-$r$ limit of the anomalous dimension for fixed rapidities and the $x$-dependence of the saturation scale.

Leptonic dark energy and baryogenesis

We consider a baryogenesis scenario, where the difference of baryon (B) and lepton (L) number is conserved in such a way that the B-L asymmetry in the standard model sector is compensated by an asymmetry of opposite sign stored in the dark energy sector. Therefore, we introduce a toy-model in which a complex quintessence field carries a B-L asymmetry at late times. We determine the produced baryon asymmetry in the visible sector for a large range of initial conditions and find it easy to achieve a value of the observed order of magnitude. While the size of the produced baryon asymmetry depends on details of the underlying inflationary model, it turns out to be independent of the reheating temperature in many cases. We also discuss possible sources of instability like the formation of Q-Balls.

Contact pressure models for spiral phyllotaxis and their computer simulation

We present a simple, biologically motivated model for the creation of phyllotactical patterns in capitula and their computer simulation. An in-depth investigation of Ridley's contact pressure model is performed and a refinement of contact pressure between primordia on the basis of local centroidal Voronoi relaxation is presented. Using this method in combination with Hofmeisters rule for placing new primordia creates stable patterns with Fibonacci spirals of high degree for a large range of initial conditions.

Verified Control of Near-Earth Asteroid Orbits

Orbit calculations of near-earth asteroids pose several difficult challenges. First of all, due to the fact that the impact of such an object is potentially serious, the problem requires as precise an answer as possible, for a relatively large range of initial conditions determined by measurement inaccuracies. Secondly, while the primary force to govern the equation of motion is the gravity of the sun, there are many other factors to influence the details of asteroid motion, making the resulting ODE quite complicated. Thirdly, based on the guaranteed prediction of the near-earth passage, a control of the asteroid orbit has to be provided if necessary, which requires verified global optimizations to determine the timing and the direction and intensity of the momentum transfer. In this paper, we outline an approach to exclude collisions or determine the minimum amount of momentum transfer necessary for their avoidance. The approach is based on verified ODE integration and verified global optimization based on the Taylor Model approach.

A novel and practical strategy for the precise chamferless robotic peg hole insertion

SummaryThe influence of the angle between the axes of the peg and hole (angular error) and the contact surface defects on the measurement of deviation (lateral error) have been carefully analysed. It has been shown that they would influence the measurement of the magnitude of deviation and even its direction. This phenomenon causes severe difficulty in the assembly operations. A novel strategy for the high-precision chamferless peg hold insertion with a wrist force sensor is presented. This strategy is constructed: (1) to obtain the relationship between the peg and hole from the force sensor signal when an angle between the axes of the peg and hole exists and defects of the contact surfaces are present, (2) to reduce the angular and lateral errors, (3) to achieve the precise chamferless robotic peg hole insertion. In this paper, the insertion can be obtained with a reasonably large range of initial conditions. The principle is to move and rotate the peg from an area having many geometric uncertainties to a new area, where the deviation of the peg and hole can be obtained.

Robotic Peg-Hole Insertion Operations using a Six-Component Force Sensor

Peg-hole insertion is a widely used industrial robot process. For precise insertion it is common to use force sensors to obtain the deviation between the peg and the hole. In this paper, several examples of six-component force sensors, which are designed to measure the forces and torques in all directions, are reviewed. The problem of how to obtain the deviation between the peg and the hole from the measurement of the forces and the torques exerted on the sensors is then discussed. It is shown that the angle between the peg and the hole and the roughness of the contact surfaces (the end surface of the peg and the surface surrounding the hole) would significantly influence the identification of deviation, no matter how small they are. Two measures to address these phenomena are introduced. A novel strategy of the high-precision chamferless peg-hole insertion with a wrist force sensor is presented and verified experimentally. This strategy is constructed: to obtain the relationship between the peg and hole from the force sensor signal when angular misalignment and the defects of the contact surfaces are present to reduce the angular and lateral errors and to achieve precise chamferless robotic peg-hole insertion. In this paper, it is shown that the insertion can be effected with a reasonably large range of initial conditions. The principle is to move and rotate the peg from an area having many geometric uncertainties to a new area, where the deviation of the peg and hole can be obtained.

Optical performance models for FDDI links

Abstract A loss budget model has been developed to predict optical perjormnce of the fiber distributed-data interjace (FDDI) type of networks in the premises-distribution environment. This model tailors existing statistical loss budget models to the FDDI standard. It is expected that as FDDI becomes popular, fiber-based distribution systems will become common. When designing a fiber-distribution system, it is important to understand the constraints placed on link perjormance by the cable plant. To determine these constraints, the model is examined numerically using a large range of initial conditions. The total link length is used as the dependent variable. This set of initial conditions corresponds to an ensemble ofpossible link configurations, and these link configurations are studied in the context of the premises-distribution environment. The model is extended to include the use of optical bypass switches. Laboratory measurement data are presented to verify the accuracy of the bypass switch model. The...