The influence of inclinations on the dynamical stability of multi-planet systems

2019 ◽  
Vol 490 (1) ◽  
pp. 359-370 ◽  
Author(s):  
Ying Wang ◽  
Ji-lin Zhou ◽  
Fu-yao Liu ◽  
Wei Sun ◽  
Hui-Gen Liu ◽  
...  
Keyword(s):  
Time Scales ◽  
Orbital Period ◽  
Time Scale ◽  
Empirical Formula ◽  
Dynamical Stability ◽  
Critical Space ◽  
Planetary Mass ◽  
The Stability ◽  
Space Separation ◽  
Comprehensive Study

ABSTRACT A type of compactly spaced and comparably sized multi-exoplanet system similar to TRAPPIST-1 has been discovered recently. The stability of these systems is an important issue, requiring further study. We examined how the initial inclinations influence the stability of multi-planet systems and derived an empirical formula describing the dependence of the instability time-scale on planetary mass, space separation and initial inclination. We find the following. (i) If space separations between planets are greater than 12RH (mutual Hill radius), coplanar multi-planet systems with 10−6 ≤ μ ≤ 10−3 (reduced planetary mass μ = m/M*) will remain stable within 1010Tin (the innermost orbital period). (ii) If initial inclinations of planets are smaller than 10° and space separations are greater than 10RH, multi-planet systems consisting of ≥5 planets with μ ≥ 10−5 will remain stable within 1010Tin. (iii) Initial inclinations in [0°, 10°] have inconsequential effects on the instability time-scales of massive multi-planet systems (μ ≥ 10−5), because eccentricities (excited during evolution) dominate the stability of these systems. (iv) If the initial inclinations are large enough (≥10°), sharp increases of instability time-scales in groups with 10−3 ≥ μ ≥ 10−5 will be moderated. This article presents a comprehensive study of the influence of inclination on the stability of multi-planet systems and discusses critical space separations for a multi-planet system becoming unstable.

scholarly journals The Stability of Mars’s Annular Polar Vortex

2017 ◽  
Vol 74 (5) ◽  
pp. 1533-1547 ◽  
Author(s):  
William J. M. Seviour ◽  
Darryn W. Waugh ◽  
Richard K. Scott
Keyword(s):  
Relaxation Time ◽  
Time Scales ◽  
Time Scale ◽  
Thermal Relaxation ◽  
Polar Vortex ◽  
Radiative Relaxation ◽  
Equilibrium Profile ◽  
Rotating Shallow Water ◽  
The Stability ◽  
Topographic Forcing

Abstract The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising, since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here the stability of a Mars-like annular vortex is investigated using numerical integrations of the rotating shallow-water equations. The mode of instability and its growth rate is shown to depend upon the latitude and width of the annulus. By introducing thermal relaxation toward an annular equilibrium profile with a time scale similar to that of the instability, a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere can be simulated. This time scale, typically 0.5–2 sols, is similar to radiative relaxation time scales for Mars’s polar atmosphere. The persistence of an annular vortex is also shown to be robust to topographic forcing, as long as it is below a certain amplitude. It is therefore proposed that the persistence of this barotropically unstable annular vortex is permitted owing to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.

scholarly journals A pulsar-based time-scale from the International Pulsar Timing Array

2019 ◽  
Vol 491 (4) ◽  
pp. 5951-5965 ◽  
Author(s):  
G Hobbs ◽  
L Guo ◽  
R N Caballero ◽  
W Coles ◽  
K J Lee ◽  
...  
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Limiting Factor ◽  
Radio Pulsars ◽  
Pulsar Timing ◽  
The Us ◽  
The Stability ◽  
Solar System Dynamics ◽  
Noise Models ◽  
Pulsar Timing Array

ABSTRACT We have constructed a new time-scale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar time-scale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected time-scale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based time-scales are unlikely to contribute to the stability of the best time-scales over the next decade, but they will remain a valuable independent check on atomic time-scales. We also find that the stability of the pulsar-based time-scale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves.

scholarly journals Long term stability of atomic time scales

2012 ◽  
Vol 10 (H16) ◽  
pp. 209-210
Author(s):  
G. Petit ◽  
F. Arias
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Time Transfer ◽  
Long Term Stability ◽  
Relative Value ◽  
The Stability ◽  
Primary Standards ◽  
Stability And Accuracy ◽  
Atomic Time

AbstractWe review the stability and accuracy achieved by the reference atomic time scales TAI and TT(BIPM). We show that they presently are in the low 10−16 in relative value, based on the performance of primary standards, of the ensemble time scale and of the time transfer techniques. We consider how the 1 × 10−16 value could be reached or superseded and which are the present limitations to attain this goal.

Fifteen Months of Pulsar Astronomy

1969 ◽  
Vol 1 (6) ◽  
pp. 254-263 ◽  
Author(s):  
V. Radhakrishnan
Keyword(s):  
Radio Source ◽  
Time Scales ◽  
Time Scale ◽  
Repetition Rate ◽  
Pulse Amplitude ◽  
Radio Observatory ◽  
Millisecond Time Scale ◽  
The Stability ◽  
The Individual

Towards the end of February 1968 the astronomical world was staggered by a paper from the Milliard Radio Observatory at Cambridge announcing the discovery of an astonishing periodic phenomenon. The characteristics of the pulsating radio source—or pulsar as it came to be called—involved a fantastic multiplicity of time-scales. The duration of the individual events was measured in tens of milliseconds, the repetition rate was of the order of a second, the pulse amplitude showed drastic variations over times of seconds, minutes, hours and even months and, lastly, the stability of the basic periodicity indicated a time-scale of millions of years. A series of pulses from CP 1919, the first pulsar, is shown in Figure 1, and one notices here both the regularity of the pulses and the variation in their amplitude with time. When the individual pulses were observed on an expanded time-scale it was found that the pulses were made up of sub-pulses (Figure 2) and that there was considerable structure even down to a millisecond time-scale.

scholarly journals Buckling versus crystal expulsion controlled by deformation rate of particle-coated air bubbles in oil

2021 ◽  
Author(s):  
Saikat Saha ◽  
Francis Pagaud ◽  
Bernard P. Binks ◽  
Valeria Garbin
Keyword(s):  
Shelf Life ◽  
Time Scales ◽  
Time Scale ◽  
Deformation Rate ◽  
Interfacial Layer ◽  
Fast Time ◽  
Flow Conditions ◽  
The Stability ◽  
Different Time Scales ◽  
Processing Flow

Oil foams stabilized by crystallizing agents exhibit outstanding stability and show promise for applications in consumer products. The stability and mechanics imparted by the interfacial layer of crystals underpin product shelf-life, as well as optimal processing conditions and performance in applications. Shelf-life is affected by the stability against bubble dissolution over a long time scale, which leads to slow compression of the interfacial layer. In processing flow conditions, the imposed deformation is characterized by much shorter time scales. In practical situations, the crystal layer is therefore subjected to deformation on extremely different time scales. Despite its importance, our understanding of the behavior of such interfacial layers at different time scales remains limited. To address this gap, here we investigate the dynamics of single, crystal-coated bubbles isolated from an oleofoam, at two extreme timescales: the diffusion-limited timescale characteristic of bubble dissolution 10,000 s, and a fast time scale characteristic of processing flow conditions, 0.001 s. In our experiments, slow deformation is obtained by bubble dissolution, and fast deformation in controlled conditions with real-time imaging is obtained using ultrasound-induced bubble oscillations. The experiments reveal that the fate of the interfacial layer is dramatically affected by the dynamics of deformation: after complete bubble dissolution, a continuous solid layer remains; while after fast, oscillatory deformation of the layer, small crystals are expelled from the layer. This observation shows promise towards developing stimuli-responsive systems, with sensitivity to deformation rate, in addition to the already known thermo- and photo-responsiveness of oleofoams.

scholarly journals Atomic time scales TAI and TT(BIPM): present performances and prospects

2009 ◽  
Vol 5 (H15) ◽  
pp. 220-221
Author(s):  
Gérard Petit
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Time Transfer ◽  
Relative Value ◽  
The Stability ◽  
Primary Standards ◽  
Stability And Accuracy ◽  
Atomic Time

AbstractWe review the stability and accuracy achieved by the reference atomic time scales TAI and TT(BIPM). We show that they presently are at the level of a few 10−16 in relative value, based on the performance of primary standards, of the ensemble time scale and of the time transfer techniques. We consider how the 1 × 10−16 value could be reached or superseded and which are the present limitations to attain this goal.

Carbonation possibilities of Steel slags -- a review

2021 ◽  
Author(s):  
Raghavendra Ragipani ◽  
Sankar Bhattacharya ◽  
Akkihebbal K. Suresh
Keyword(s):  
Carbon Dioxide ◽  
Time Scales ◽  
Carbon Dioxide Sequestration ◽  
Mineral Carbonation ◽  
Geological Time ◽  
The Stability ◽  
Significant Attention

Research pertaining to carbon dioxide sequestration via mineral carbonation has gained significant attention, primarily due to the stability of sequestered \ce{CO2} over geological time scales. Use of industry-derived alkaline wastes...

scholarly journals GNSS-to-GNSS time offsets: study on the broadcast of a common reference time

GPS Solutions ◽  
2021 ◽  
Vol 25 (2) ◽  
Author(s):  
Ilaria Sesia ◽  
Giovanna Signorile ◽  
Tung Thanh Thai ◽  
Pascale Defraigne ◽  
Patrizia Tavella
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Reference Time ◽  
Single Time ◽  
Common Reference ◽  
Prediction Quality ◽  
Common Time ◽  
Time Offset ◽  
The Impact ◽  
Low Uncertainty

AbstractWe present two different approaches to broadcasting information to retrieve the GNSS-to-GNSS time offsets needed by users of multi-GNSS signals. Both approaches rely on the broadcast of a single time offset of each GNSS time versus one common time scale instead of broadcasting the time offsets between each of the constellation pairs. The first common time scale is the average of the GNSS time scales, and the second time scale is the prediction of UTC already broadcast by the different systems. We show that the average GNSS time scale allows the estimation of the GNSS-to-GNSS time offset at the user level with the very low uncertainty of a few nanoseconds when the receivers at both the provider and user levels are fully calibrated. The use of broadcast UTC prediction as a common time scale has a slightly larger uncertainty, which depends on the broadcast UTC prediction quality, which could be improved in the future. This study focuses on the evaluation of two different common time scales, not considering the impact of receiver calibration, at the user and provider levels, which can nevertheless have an important impact on GNSS-to-GNSS time offset estimation.

Sensor-Based Estimation of Dim Light Melatonin Onset Using Features of Two Time Scales

2021 ◽  
Vol 2 (3) ◽  
pp. 1-15
Author(s):  
Cheng Wan ◽  
Andrew W. Mchill ◽  
Elizabeth B. Klerman ◽  
Akane Sano
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Light Exposure ◽  
Biological Activities ◽  
Second Step ◽  
Sampled Data ◽  
Dim Light Melatonin Onset ◽  
Dim Light ◽  
Using Data ◽  
Mean Square Errors

Circadian rhythms influence multiple essential biological activities, including sleep, performance, and mood. The dim light melatonin onset (DLMO) is the gold standard for measuring human circadian phase (i.e., timing). The collection of DLMO is expensive and time consuming since multiple saliva or blood samples are required overnight in special conditions, and the samples must then be assayed for melatonin. Recently, several computational approaches have been designed for estimating DLMO. These methods collect daily sampled data (e.g., sleep onset/offset times) or frequently sampled data (e.g., light exposure/skin temperature/physical activity collected every minute) to train learning models for estimating DLMO. One limitation of these studies is that they only leverage one time-scale data. We propose a two-step framework for estimating DLMO using data from both time scales. The first step summarizes data from before the current day, whereas the second step combines this summary with frequently sampled data of the current day. We evaluate three moving average models that input sleep timing data as the first step and use recurrent neural network models as the second step. The results using data from 207 undergraduates show that our two-step model with two time-scale features has statistically significantly lower root-mean-square errors than models that use either daily sampled data or frequently sampled data.

scholarly journals Locally and Remotely Forced Subtropical AMOC Variability: A Matter of Time Scales

2020 ◽  
Vol 33 (12) ◽  
pp. 5155-5172
Author(s):  
Quentin Jamet ◽  
William K. Dewar ◽  
Nicolas Wienders ◽  
Bruno Deremble ◽  
Sally Close ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
North Atlantic ◽  
Time Scale ◽  
Low Frequency ◽  
Meridional Overturning Circulation ◽  
Open Boundary ◽  
Overturning Circulation ◽  
Decadal Scale ◽  
Meridional Overturning

AbstractMechanisms driving the North Atlantic meridional overturning circulation (AMOC) variability at low frequency are of central interest for accurate climate predictions. Although the subpolar gyre region has been identified as a preferred place for generating climate time-scale signals, their southward propagation remains under consideration, complicating the interpretation of the observed time series provided by the Rapid Climate Change–Meridional Overturning Circulation and Heatflux Array–Western Boundary Time Series (RAPID–MOCHA–WBTS) program. In this study, we aim at disentangling the respective contribution of the local atmospheric forcing from signals of remote origin for the subtropical low-frequency AMOC variability. We analyze for this a set of four ensembles of a regional (20°S–55°N), eddy-resolving (1/12°) North Atlantic oceanic configuration, where surface forcing and open boundary conditions are alternatively permuted from fully varying (realistic) to yearly repeating signals. Their analysis reveals the predominance of local, atmospherically forced signal at interannual time scales (2–10 years), whereas signals imposed by the boundaries are responsible for the decadal (10–30 years) part of the spectrum. Due to this marked time-scale separation, we show that, although the intergyre region exhibits peculiarities, most of the subtropical AMOC variability can be understood as a linear superposition of these two signals. Finally, we find that the decadal-scale, boundary-forced AMOC variability has both northern and southern origins, although the former dominates over the latter, including at the site of the RAPID array (26.5°N).

Sign in / Sign up

Export Citation Format

Share Document