Theoretical study on stability evolution of soft and hard interbedded bedding reservoir slopes

Soft and hard interbedded bedding rock slopes,which is prone to failure,are widely distributed in the Three Gorges Reservoir,China.Limit equilibrium method(LEM)is commonly used to analyze the stability of bedding rock slopes that have a single failure plane.However,this method cannot accurately estimate the stability of soft and hard interbedded bedding reservoir slopes because the strength parameters of a soft and hard interbedded rock mass vary spatially along the bedding plane and deteriorate with time due to periodic fluctuations of reservoir level.A modified LEM is proposed to evaluate the stability evolution of soft and hard interbedded bedding reservoir slopes considering the spatial variation and temporal deterioration of shear strength parameters of rock masses and bedding planes.In the modified LEM,the S-curve model is used to define the spatial variation of shear strength parameters,and general deterioration equations of shear strength parameters with the increasing number of wettingdrying cycles(WDC)are proposed to describe the temporal deterioration.Also,this method is applied to evaluate the stability evolution of a soft and hard interbedded bedding reservoir slope,located at the Three Gorges Reservoir.The results show that neglecting the spatial variation and temporal deterioration of shear strength parameters may overestimate slope stability.Finally,the modified LEM provides useful guidance to reasonably evaluate the long-term stability of soft and hard interbedded bedding reservoir slopes in reservoir area.

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Temporary capture efficiency is studied in the framework of the circular restricted three-body problem in two steps.First, a non-uniform distribution of test particles around the secondary's orbit is obtained by fully accounting the secondary's gravitational influence. Second, the capture efficiency is computed based on the non-uniform distribution. Several factors influencing the result are discussed. By studying the capture efficiency in the circular restricted three-body problem of different mass ratios, a power-law relation between the capture efficiency(p) and the mass ratio(μ) is established, which is given by p ≈ 0.27 × μ^(0.53), within the range of 3.0035 ×10^(-6)≤ μ ≤ 3.0034 × 10^(-5). Taking the Sun–Earth system as an example, the influence from the orbit eccentricity of the secondary on the non-uniform distribution and the capture efficiency is studied. Our studies find that the secondary's orbit eccentricity has a negative influence on the capture efficiency.

The Investigation of the Dynamical Evolution of Extrasolar Three-planetary System GJ 3138

This article is devoted to studying the dynamical evolution and orbital stability of compact extrasolar threeplanetary system GJ 3138. In this system, all semimajor axes are less than 0.7 au. The modeling of planetary motion is performed using the averaged semi-analytical motion theory of the second order in planetary masses,which the authors construct. Unknown and known with errors orbital elements vary in allowable limits to obtain a set of initial conditions. Each of these initial conditions is applied for the modeling of planetary motion. The assumption about the stability of observed planetary systems allows to eliminate the initial conditions leading to excessive growth of the orbital eccentricities and inclinations and to identify those under which these orbital elements conserve moderate values over the whole modeling interval. Thus, it becomes possible to limit the range of possible values of unknown orbital elements and determine their most probable values in terms of stability.

Stability of the coplanar planetary four-body system

We consider the coplanar planetary four-body problem,where three planets orbit a large star without the cross of their orbits.The system is stable if there is no exchange or cross of orbits.Starting from the Sundman inequality,the equation of the kinematical boundaries is derived.We discuss a reasonable situation,where two planets with known orbits are more massive than the third one.The boundaries of possible motions are controlled by the parameter c^2E.If the actual value of c^2E is less than or equal to a critical value(c^2 E)cr,then the regions of possible motions are bounded and therefore the system is stable.The criteria obtained in special cases are applied to the Solar System and the currently known extrasolar planetary systems.Our results are checked using N-body integrator.

Effect of Orbital Characteristic of Inclined Third-body on Motion of Secondary-body for a Hierarchical Triple Systems

The influence of a third-body's orbital elements on the second-body's motion in a hierarchical triple system is a crucial problem in astrophysics.Most prolonged evaluation studies have focused on a distant zero-inclined thirdbody.This study presents a new perspective on second-body motion equations that addresses a perturbing-body in an elliptic orbit derived with consideration of the axial-tilt(obliquity)of the primary.The proposed model is compared by the dual-averaged method and the N-body problem algorithm.After validation,a generalized threebody model is derived to investigate the effects of the third-body's orbital elements on secondary-body motion behavior.The proposed model considers short-time oscillations that affect secular evaluation and applies to exoplanets with all the primary and third body eccentricities,inclinations,and mass ratios.It is shown that the obliquity of the primary(or third-body's inclination)must be considered for precise long-term assessment,even in highly-hierarchical systems.

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.

A tale of planet formation: from dust to planets

The characterization of exoplanets and their birth protoplanetary disks has enormously advanced in the last decade.Benefitting from that,our global understanding of the planet formation processes has been substantially improved.In this review,we first summarize the cutting-edge states of the exoplanet and disk observations.We further present a comprehensive panoptic view of modern core accretion planet formation scenarios,including dust growth and radial drift,planetesimal formation by the streaming instability,core growth by planetesimal accretion and pebble accretion.We discuss the key concepts and physical processes in each growth stage and elaborate on the connections between theoretical studies and observational revelations.Finally,we point out the critical questions and future directions of planet formation studies.

A semi-analytic model for the study of 1/1 resonant dynamics of the planar elliptic restricted co-orbital problem

Mean motion resonances(MMRs)are widespread in our Solar System.Moreover,resonant dynamics has always been an essential topic in planetary research.Recently,the research about exoplanets and the potential Planet Nine with large eccentricity has given rise to our interests in the secular dynamics inside MMRs in the elliptic model.In this paper,we study the fixed points of the averaged Hamiltonian and the long-term stable regions of the 1/1 resonance(or co-orbital motion)in the elliptic restricted three-body problem(ERTBP)systematically.Numerical integrations prove those test particles trapped in"apsidal co-rotation",where both the resonant angleφ_(res)and the secular angleΔω(or apsidal longitude differences)librate simultaneously,always survive the long-term simulations.Furthermore,utilizing a semianalytical method based on the adiabatic approach,three families of long-term fixed points of the averaged Hamiltonian of the planar ERTBP inside the 1/1 resonance have been found.We call them QS-points,Hpoints,and T-points here,whose values of the(φ_(res),Δω)are(0°,180°),(180°,0°),and(±60°,±60°),respectively.All the fixed points of the averaged Hamiltonian of the co-orbital motion in the ERTBP are presented in the e-e’plane(’represents the elements of the planet in this paper).We find that QS-points and T-points always exist for the arbitrary eccentricity of a planet,while H-points only exist for the cases of low e’and very high e.Furthermore,we measure the libration width in terms of eccentricity,Δe,around these stable equilibrium points in the e-Δωphase-space portraits.The"apsidal co-rotation"around all the stable equilibrium points is presented in the e-e’plane.All these results are effectively confirmed by numerical experiments.The long-term stable zones around these periodic orbits in the e-e’plane are significant for the research of the co-orbital motion in the ERTBP.Above all,these practical approaches that we proposed can also be used to study the secular dynamics of other MMRs.

Forming different planetary systems

With the increasing number of detected exoplanet samples, the statistical properties of planetary systems have become much clearer. In this review, we sum- marize the major statistical results that have been revealed mainly by radial velocity and transiting observations, and try to interpret them within the scope of the classical core-accretion scenario of planet formation, especially in the formation of different orbital architectures for planetary systems around main sequence stars. Based on the different possible formation routes for different planet systems, we tentatively classify them into three major catalogs： hot Jupiter systems, standard systems and distant giant planet systems. The standard systems can be further categorized into three sub-types under different circumstances： solar-like systems, hot Super-Earth systems, and sub- giant planet systems. We also review the theory of planet detection and formation in binary systems as well as planets in star clusters.

Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem

The restricted three-body problem(RTBP) is a fundamental model in celestial mechanics.Periodic orbits in the synodic frame play a very important role in understanding the dynamics of the RTBP model.Most of these periodic orbits,when interpreted in the sidereal frame,are actually resonant periodic orbits.As a result,numerical computation of the periodic orbits is also one approach for researchers to understand the orbital resonances of the three-body problem.Extensive studies have been carried out on this topic,concerning either the circular case or the elliptic case of this model.In this paper,we make a brief review of the history and current status of the studies on resonant periodic orbits in the RTBP model.Starting from the unperturbed two-body problem,we organize the review paper by the two cases of this model—the circular restricted three-body problem and the elliptic restricted three-body problem.

High-performance Bi_(2)S_(3)/ZnO photoanode enabled by interfacial engineering with oxyanion for efficient photoelectrochemical water oxidation

In the present contribution,we demonstrate that the sluggish kinetics of oxygen evolution reaction(OER)over the bismuth sulfide(Bi_(2)S_(3))photoanode,which severely restricts its photoelectrochemical activity,is markedly accelerated by employing a sulfatecontaining electrolyte.First-principle calculation points to the spontaneous adsorption of sulfate(SO_(4)^(2−))on Bi_(2)S_(3)and its capacity of stabilizing the OER intermediates through hydrogen bonding,which is further reinforced by increasing the local density of states near the Fermi level of Bi_(2)S_(3).Meanwhile,the electron transfer is also promoted to synergistically render the ratedetermining step(from O*to OOH*)of OER over Bi_(2)S_(3)kinetically facile.Last but not least,benefitting from such enhanced OER activity and efficient charge separation resulted from depositing Bi_(2)S_(3)on the zinc oxide nanorods(ZnO NRs),forming a core–shell heterojunction,its photocurrent density achieves 8.61 mA·cm^(−2)at 1.23 VRHE,far surpassing those reported for additional Bi_(2)S_(3)-based and several state-of-the-art photoanodes in the literature and further exceeding their theoretical limit.The great promise of the Bi_(2)S_(3)/ZnO NRs is in view of such outperformance,the superior Faradaic yield of oxygen of more than~80%and the outstanding half-cell applied bias photon-to-current efficiency of~1%well corroborated.