scholarly journals Secular evolution of close-in planets: the effects of general relativity

2020 ◽  
Vol 493 (1) ◽  
pp. 427-436
Author(s):  
F Marzari ◽  
M Nagasawa
Keyword(s):  
General Relativity ◽  
Numerical Integration ◽  
Time Scales ◽  
Initial Conditions ◽  
Outer Planet ◽  
Secular Perturbations ◽  
Secular Evolution ◽  
Eccentric Orbits ◽  
Wide Range ◽  
Comparable Time

ABSTRACT Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet–planet scattering, Kozai, or secular migration. In this scenario, general relativity and secular perturbations have comparable time-scales and may interfere with each other with relevant effects on the eccentricity and pericenter evolution of the two planets. We explore, both analytically and via numerical integration, how the secular evolution is changed by general relativity for a wide range of different initial conditions. We find that when the faster secular frequency approaches the general relativity precession rate, which typically occurs when the outer planet moves away from the inner one, it relaxes to it and a significant damping of the proper eccentricity of the inner planet occurs. The proper eccentricity of the outer planet is reduced as well due to the changes in the secular interaction of the bodies. The lowering of the peak eccentricities of the two planets during their secular evolution has important implications on their stability. A significant number of two-planet systems, otherwise chaotic because of the mutual secular perturbations, are found stable when general relativity is included.

scholarly journals Trojans in Exosystems with Two Massive Planets

2012 ◽  
Vol 8 (S293) ◽  
pp. 152-158 ◽  
Author(s):  
Rudolf Dvorak ◽  
Li-Yong Zhou ◽  
Helmut Baudisch
Keyword(s):  
Numerical Integration ◽  
Equilibrium Points ◽  
Planetary Systems ◽  
Central Star ◽  
Giant Planets ◽  
Dynamical Model ◽  
Outer Planet ◽  
Mass Ratio ◽  
Wide Range ◽  
Mass Ratios

AbstractWe take as dynamical model for extrasolar planetary systems a central star like our Sun and two giant planets m1 and m2 like Jupiter and Saturn. We change the mass ratio μ=m2/m1 of the two large planets for a wide range of 1/16 < μ < 16. We also change the ratio between the initial semi-major axes (ν=a2/a1) in the range of 1.2 < ν < 3 to model the different architecture of extrasolar planetary systems hosting two giant planets. The results for possible Trojans (Trojan planets) in the equilateral equilibrium points of the inner planet m1 and the outer planet m2 were derived with the aid of numerical integration. It turned out that in many configurations – depending on the mass ratios μ and the semi-major axes ratio ν – giant planets may host Trojans.

scholarly journals Influence of general-relativity effects, dynamical tides, and collisions on planet–planet scattering close to the star

2019 ◽  
Vol 625 ◽  
pp. A121 ◽  
Author(s):  
F. Marzari ◽  
M. Nagasawa
Keyword(s):  
General Relativity ◽  
Numerical Integration ◽  
Semimajor Axis ◽  
Central Star ◽  
Giant Planets ◽  
Circular Orbits ◽  
Dynamical Mechanism ◽  
Tidal Interactions ◽  
Eccentric Orbits ◽  
Scattering Events

Context. Planet–planet (P–P) scattering is an efficient and robust dynamical mechanism for producing eccentric exoplanets. Coupled to tidal interactions with the central star, this phenomenon can also explain close-in giant planets on circularized and potentially misaligned orbits. Aims. We explore scattering events occurring close to the star and test if they can reproduce the main features of the observed orbital distribution of giant exoplanets on tight orbits. Methods. In our modeling we exploited a numerical integration code based on the Hermite algorithm and including the effects of general relativity, dynamical tides, and two-body collisions. Results. We find that P–P scattering events occurring in systems with three giant planets initially moving on circular orbits close to their star produce a population of planets similar to that presently observed, including eccentric and misaligned close-in planets. The contribution of tides and general relativity is relevant in determining the final outcome of the chaotic phase. Conclusions. Even if two-body collisions dominate the chaotic evolution of three planets in crossing orbits close to their star, the final distribution shows a significant number of planets on eccentric orbits. The highly misaligned close-in giant planets are instead produced by systems where the initial semimajor axis of the inner planet was around 0.2 au or beyond.

scholarly journals On the generation of internal waves by river plumes in subcritical initial conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Mendes ◽  
J. C. B. da Silva ◽  
J. M. Magalhaes ◽  
B. St-Denis ◽  
D. Bourgault ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Internal Waves ◽  
Coastal Waters ◽  
Initial Conditions ◽  
Spatial Scales ◽  
River Plumes ◽  
Wide Range ◽  
Near Shore ◽  
Generation Mechanisms ◽  
Douro River

AbstractInternal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

scholarly journals Harmonic hybrid inflation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Federico Carta ◽  
Nicole Righi ◽  
Yvette Welling ◽  
Alexander Westphal
Keyword(s):  
Domain Wall ◽  
Symmetry Breaking ◽  
Initial Conditions ◽  
Scalar Potential ◽  
Field Range ◽  
Slow Roll ◽  
Minimal Form ◽  
Wide Range ◽  
Hybrid Inflation ◽  
Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

Numerical investigation of the propagation of shock waves in rigid porous materials: development of the computer code and comparison with experimental results

1996 ◽  
Vol 324 ◽  
pp. 163-179 ◽  
Author(s):  
A. Levy ◽  
G. Ben-Dor ◽  
S. Sorek
Keyword(s):  
Porous Materials ◽  
Initial Conditions ◽  
Computer Code ◽  
Experimental Results ◽  
Numerical Code ◽  
Materials Development ◽  
Numerical Predictions ◽  
Wide Range ◽  
Dimensional Version ◽  
The One

The governing equations of the flow field which is obtained when a thermoelastic rigid porous medium is struck head-one by a shock wave are developed using the multiphase approach. The one-dimensional version of these equations is solved numerically using a TVD-based numerical code. The numerical predictions are compared to experimental results and good to excellent agreements are obtained for different porous materials and a wide range of initial conditions.

scholarly journals PNA Predictability at Various Time Scales

2013 ◽  
Vol 26 (22) ◽  
pp. 9090-9114 ◽  
Author(s):  
Waqar Younas ◽  
Youmin Tang
Keyword(s):  
Time Scales ◽  
Initial Conditions ◽  
Prediction Skill ◽  
Multiple Model ◽  
Coupled Models ◽  
Potential Predictability ◽  
Effective Measure ◽  
Dispersion Component ◽  
Significant Difference ◽  
Better Than

Abstract In this study, the predictability of the Pacific–North American (PNA) pattern is evaluated on time scales from days to months using state-of-the-art dynamical multiple-model ensembles including the Canadian Historical Forecast Project (HFP2) ensemble, the Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER) ensemble, and the Ensemble-Based Predictions of Climate Changes and their Impacts (ENSEMBLES). Some interesting findings in this study include (i) multiple-model ensemble (MME) skill was better than most of the individual models; (ii) both actual prediction skill and potential predictability increased as the averaging time scale increased from days to months; (iii) there is no significant difference in actual skill between coupled and uncoupled models, in contrast with the potential predictability where coupled models performed better than uncoupled models; (iv) relative entropy (REA) is an effective measure in characterizing the potential predictability of individual prediction, whereas the mutual information (MI) is a reliable indicator of overall prediction skill; and (v) compared with conventional potential predictability measures of the signal-to-noise ratio, the MI-based measures characterized more potential predictability when the ensemble spread varied over initial conditions. Further analysis found that the signal component dominated the dispersion component in REA for PNA potential predictability from days to seasons. Also, the PNA predictability is highly related to the signal of the tropical sea surface temperature (SST), and SST–PNA correlation patterns resemble the typical ENSO structure, suggesting that ENSO is the main source of PNA seasonal predictability. The predictable component analysis (PrCA) of atmospheric variability further confirmed the above conclusion; that is, PNA is one of the most predictable patterns in the climate variability over the Northern Hemisphere, which originates mainly from the ENSO forcing.

MODELING NANOSECOND-PULSED SPARK DISCHARGE AND FLAME KERNEL EVOLUTION

2021 ◽  
pp. 1-22
Author(s):  
Joohan Kim ◽  
Vyaas Gururajan ◽  
Riccardo Scarcelli ◽  
Sayan Biswas ◽  
Isaac Ekoto
Keyword(s):  
Electrical Discharge ◽  
Internal Combustion Engines ◽  
Initial Conditions ◽  
Fuel Mixture ◽  
Spark Ignition ◽  
Combustion Stability ◽  
Flame Kernel ◽  
Wide Range ◽  
Challenging Environment ◽  
Kernel Growth

Abstract Dilute combustion, either using exhaust gas recirculation or with excess-air, is considered a promising strategy to improve the thermal efficiency of internal combustion engines. However, the dilute air-fuel mixture, especially under intensified turbulence and high-pressure conditions, poses significant challenges for ignitability and combustion stability, which may limit the attainable efficiency benefits. In-depth knowledge of the flame kernel evolution to stabilize ignition and combustion in a challenging environment is crucial for effective engine development and optimization. To date, comprehensive understanding of ignition processes that result in the development of fully predictive ignition models usable by the automotive industry does not yet exist. Spark-ignition consists of a wide range of physics that includes electrical discharge, plasma evolution, joule-heating of gas, and flame kernel initiation and growth into a self-sustainable flame. In this study, an advanced approach is proposed to model spark-ignition energy deposition and flame kernel growth. To decouple the flame kernel growth from the electrical discharge, a nanosecond pulsed high-voltage discharge is used to trigger spark-ignition in an optically accessible small ignition test vessel with a quiescent mixture of air and methane. Initial conditions for the flame kernel, including its thermodynamic state and species composition, are derived from a plasma-chemical equilibrium calculation. The geometric shape and dimension of the kernel are characterized using a multi-dimensional thermal plasma solver. The proposed modeling approach is evaluated using a high-fidelity computational fluid dynamics procedure to compare the simulated flame kernel evolution against flame boundaries from companion schlieren images.

scholarly journals Internal volumetric heat generation and heat capacity prediction during a material electromagnetic treatment process using hybrid algorithms

2018 ◽  
Vol 38 (1) ◽  
pp. 74-82
Author(s):  
Edgar García-Morantes ◽  
Iván Amaya-Contreras ◽  
Rodrigo Correa-Cely
Keyword(s):  
Inverse Problem ◽  
Heat Capacity ◽  
Electromagnetic Field ◽  
Heat Generation ◽  
Initial Conditions ◽  
Limited Range ◽  
First Case ◽  
Realistic Situation ◽  
Wide Range ◽  
Volumetric Heat Generation

This work considers the estimation of internal volumetric heat generation, as well as the heat capacity of a solid spherical sample, heated by a homogeneous, time-varying electromagnetic field. To that end, the numerical strategy solves the corresponding inverse problem. Three functional forms (linear, sinusoidal, and exponential) for the electromagnetic field were considered. White Gaussian noise was incorporated into the theoretical temperature profile (i.e. the solution of the direct problem) to simulate a more realistic situation. Temperature was pretended to be read through four sensors. The inverse problem was solved through three different kinds of approach: using a traditional optimizer, using modern techniques, and using a mixture of both. In the first case, we used a traditional, deterministic Levenberg-Marquardt (LM) algorithm. In the second one, we considered three stochastic algorithms: Spiral Optimization Algorithm (SOA), Vortex Search (VS), and Weighted Attraction Method (WAM). In the final case, we proposed a hybrid between LM and the metaheuristics algorithms. Results show that LM converges to the expected solutions only if the initial conditions (IC) are within a limited range. Oppositely, metaheuristics converge in a wide range of IC but exhibit low accuracy. The hybrid approaches converge and improve the accuracy obtained with the metaheuristics. The difference between expected and obtained values, as well as the RMS errors, are reported and compared for all three methods.

scholarly journals FRATs: Searching for fast radio transient in real-time with LOFAR

2012 ◽  
Vol 8 (S291) ◽  
pp. 233-233
Author(s):  
Heino Falcke ◽  
Keyword(s):  
Time Scales ◽  
Search Space ◽  
Large Field ◽  
New Radio ◽  
Wide Range ◽  
Imaging Observation ◽  
Previous Decade ◽  
First Results ◽  
Single Radio ◽  
Radio Transients

AbstractLOFAR is an innovative new radio interferometer operating at low radio frequencies from 10 to 270 MHz. It combines a large field-of-view, high fractional bandwidth, rapid response, and a wide range of baselines from tens of meters to thousand kilometers. Its use of phased-array technology and its digital nature make LOFAR an extremely versatile instrument to search for transient radio phenomena on all time scales. Here we discuss in particular the search for fast radio transients (FRATs) at sub-second time scales. In fact, at these time scales the radio sky is rather dynamic due to coherent emission processes. Objects like pulsars, flaring stars, or planets like Jupiter are able to produce bright short flares. For pulsars, most previous detection strategies made use of the rotation of pulsars to detect them, using Fourier techniques, but it is also possible to detect pulsars and other objects through their single pulses. Such surveys have, e.g., led in the previous decade to the detection of Rapid Radio Transients (RRATS), but the unprobed search space is still rather large. LOFAR is now conducting a rather unique survey over the entire northern sky, searching for bright dispersed single radio pulses. This FRATs survey makes use of the LOFAR transient buffer boards (TBBs), which had initially been used to detect nanosecond radio pulses from cosmic rays. The TBBs store the radio data from each single receiver element of LOFAR and allow one to look back in time. A trigger system that runs parallel to normal imaging observation allows one to detect single pulses in an incoherent beam of all LOFAR stations, covering several tens to hundred square degrees at once. Once triggered, the data can be used to localize the pulse and to discriminate cosmic sources from terrestrial interference through 3D localization. The system has been successfully tested with known pulsars and first results of the ongoing survey will be presented.

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