Secular Stability Research Articles

Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Multiple analytical, semi-analytical, and empirical stability criteria have been derived in the literature for two-planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two-planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semimajor axis of the inner binary β = δ a 1/a 1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of β ∼ 0.01 can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to von Ziepel–Lidov–Kozai (vZLK) dynamics; and (3) mean motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age.

NEW APPROACH TOWARDS THE PROBLEM OF SOMATIC CRITERIA OF SECULAR TRENDS. SEXUAL SOMATIC DIMORPHISM

Introduction. The goal of study is description of secular dynamics of sex dimorphism (SD) of height, weight, chest girth of children aged 9 years and teenagers 13 years old from Russia and neighboring countries through 1920–2010. Materials and methods. The main source of data — materials of books on physical development of children and adolescents from cities and rural regions of Russia and USSR, collected and processed according to the universal methodical standards of Research Institute of Hygiene of children and adolescents. The quantitative estimation of SD value was held using Kullback divergence. One-year age groups, contrastive in biological essence, are under discussion. The estimation of the vector and level of associations of SD of anthropometric traits and secular factor was held using correlation analysis. The analysis of local patterns of secular SD dynamics of separate traits was carried out. Results. Secular variability of height and weight SD of 9-year-old children is not significant. While secular dynamics of three body dimensions of 13-year-old teenagers is significant, the highest determination coefficient is fixed for weight. For Moscow samples the decrease of height and weight SD is fixed through the historic interval 1960s – 70s with the following recovery up to the level of 1920s in 2000s. Temporal dynamics of SD of 9-year-old children of St. Petersburg through the interval 1960s – 2000s consists of macrosomization of girls; the tendency for 13-year-old teenagers is opposite. Temporal dynamics of somatic SD of 9-year-old Russian children of Kazan reveals stability through the interval 1960th-1990th; for 13-year-old teenagers’ parameters of transversal body development demonstrate secular stability, as to height – boys compensate their lag compared to girls. For Kirovsk city (Murmansk region) through the interval 1950s – 1970s temporal fluctuations of height and weight SD of 9-year-old children are less than 0,2 standard deviations; height and weight SD of 13-year-old teenagers reveal temporal increase (0,4–0,6 standard deviations). Conclusion. The results confirm the importance of somatic SD as the criterion of secular dynamics for 13-year-old teenagers and witness, as a whole, to the temporal stability of SD during second childhood (9 years). Local differences do not contribute significantly to the intensity of secular dynamics of SD. The process of secular macrosomization of one sex as compared to the other is not the exclusive prerogative of boys and male teenagers.

Extremely Inclined Orbit of the S-type Planet γ Cep Ab Induced by the Eccentric Kozai–Lidov Mechanism

γ Cep Ab is a typical S-type planet, which occupies a nearly perpendicular planetary orbit relative to the binary. Here, we use a Markov Chain Monte Carlo sampler to conduct a full N-body fitting and derive self-consistent orbital solutions for this hierarchical system. We then employ the eccentric Kozai–Lidov (EKL) mechanism to explain the extremely inclined orbit of the S-type planet γ Cep Ab. The EKL mechanism plays an essential part in our exploration of the significant oscillations of the mutual inclination i mut between the planet and the secondary star. We perform a qualitative analysis and use extensive numerical integrations to investigate the flip conditions and timescales of γ Cep Ab’s orbit. When the planetary mass is 15 M Jup, the planet can reach i mut ∼ 113° given the critical initial conditions of i mut < 60° and e 1 < 0.7. The timescale for the first orbital flip decreases with the increase of the perturbation Hamiltonian. The flipping orbits of γ Cep Ab are confirmed to have a large possibility of remaining stable, based on surfaces of section and the secular stability criterion. Furthermore, we extend the application of EKL to general S-type planetary systems with a 1/a 2 ≤ 0.1, where the most intense excitation of i mut occurs when a 1/a 2 = 0.1 and e 2 ∼ 0.8, and the variation in planetary mass mainly affects the flip possibility where e 1 ≤ 0.3.

Secular Trend of Body Dimensions in Highly Qualified Wrestlers

The purpose of the paper was to study the physique of highly qualified martial art athletes engaged in different types of wrestling, and to perform a retrospective analysis of the morphological characteristics of wrestlers examined since the early 1920s. The materials of the anthropometric survey of 48 athletes engaged in different types of wrestling with qualification from the candidate for master of sports and above were used for this purpose and compared to the "control group" of young men (N = 97) who were not engaged in sports (similar to the group of athletes by age, ethnicity and percentage of individuals with different weight categories). A set of morphological traits was established that contributed to the successful achievements in sports. When comparing the physique of modern athletes with that of the wrestlers surveyed in the early and mid-20th century (the 1920s and 1960s), it has been shown that the secular trend towards increase in height typical for modern population, was expressed in athletes to a much lesser extent. Striking similarities were revealed for absolute and relative dimensions characterizing the skeletal body proportions of the wrestlers, which pointed to the secular stability of this sports morphotype. The obtained results can be used as additional morphological criteria for sports selection, professional orientation and prediction of competitive success.

Эпохальный ретроспективный анализ показателей телосложения у спортсменов-единоборцев высокой квалификации

Introduction. The purpose of the paper was to study the physique of highly qualified martial art athletes engaged in different types of wrestling, and to perform a retrospective analysis of the morphological fea-tures of wrestlers examined since the early 1920s. Materials and methods. Anthropometric data of 48 male athletes who were engaged in martial arts (different types of wrestling) for many years and reached high qualifications (from a candidate for master of sports and above) were used in this study. Athletes were 18-31 years old (mean age – 20.62±0.43), almost all of Russian ethnicity, permanent residents of Moscow. For comparative analysis, the materials of the anthro-pometric survey of young men – students of different Moscow universities were taken (N = 97). The stu-dents were not involved in sports, were of the same age (20.19±0.29), of Russian ethnicity and represented with different weight categories. They were used as a "control group". Results. On the materials of the anthropometric survey of athletes engaged in different types of wrestling, in comparison with the so-called "control group", a set of morphological features was established contrib-uting to the successful achievement in sports. When comparing the physique of modern athletes and wres-tlers surveyed in the early and middle of the last century (1920s and 1960s), it is shown that the trend of the secular increase in height typical for modern population, is expressed in athletes to a much lesser extent. Striking similarities are revealed for absolute and relative dimensions characterizing the skeletal body pro-portions of the wrestlers, which indicates the secular stability of this sports morphotype. Conclusion. The obtained results demonstrate the patterns of formation of morphological features and secular stability of the morphotype of highly qualified athletes involved in different types of wrestling. Re-vealed complex of somatic features can be used as additional morphological criteria for sports selection, professional orientation and prediction of competitive success.

Orbital Stability Around the Primary of a Binary Asteroid System

Orbiting the primary of a binary asteroid system is extremely challenging due to the perturbative effects of the primary’s nonspherical gravity and the secondary’s close-proximity third-body gravity. In this work, the stability of perturbed Keplerian orbits around the primary is investigated from the point of view of the long-term eccentricity oscillation. Numerical investigations indicate that the eccentricity undergoes a large-amplitude oscillation, caused by the secular perturbation of the secondary’s gravity and may cause impact. A two-degree-of-freedom dynamic model is established, based on the doubly averaged, semi-analytical orbital dynamics incorporating effects of the primary’s oblateness and the secondary’s nonspherical third-body gravity. The oscillation of eccentricity, including its phase and amplitude, and its dependence on initial orbital geometry, is investigated through the phase space structure. The results can reveal the origin of the instability, predict stable and unstable regions in the space of orbital elements, and determine the initial orbital geometry that can ensure the secular stability. The binary asteroid system 2003 YT1 is used as an example to present our verifications and analyses, and the results can also be applied to other binary asteroid systems and even planetary systems with the central body’s oblateness and the third-body gravity dominating the perturbative environments.

MXene@Ag-based ratiometric electrochemical sensing strategy for effective detection of carbendazim in vegetable samples

In this paper, a novel ratiometric electrochemical sensor for carbendazim (CBZ) detection was constructed by a composite of MXene@Ag nanoclusters and amino-functionalized multi-walled carbon nanotubes (MXene@AgNCs/NH2-MWCNTs). The Ag nanoclusters (AgNCs) embedded in the MXene not only could inhibit the aggregation of MXene flakes and enhance the electrocatalytic ability, but also serve as an internal reference probe for the ratiometric electrochemical detection. Moreover, the introduction of NH2-MWCNTs can further improve the electrochemical signals of CBZ and Ag, resulting in the enhanced signal amplification and higher sensitivity. Based on these characteristics of the MXene@AgNCs/NH2-MWCNTs composite, the proposed sensor exhibits a favorable linear relationship between ICBZ/IAgNCs and the concentration of CBZ ranging from 0.3 nM to 10 μM and a low limit of detection of 0.1 nM. Moreover, the proposed ratiometric electrochemical sensing platform also demonstrates high selectivity, good reproducibility, secular stability, and satisfactory applicability in vegetable samples.

High order explicit Lorentz invariant volume-preserving algorithms for relativistic dynamics of charged particles

Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct structure-preserving algorithms, but without exquisite considerations, it can easily break the Lorentz invariance of continuous systems. In this paper, we introduce a Lorentz invariant splitting technique to construct high order explicit Lorentz invariant volume-preserving algorithms (LIVPAs) for simulating charged particle dynamics. Using this method, long-term stable explicit LIVPAs with different orders are developed and their performances of Lorentz invariance and long-term stability are analyzed in detail.

Secular Stability of the Magnetic Structures of Magnetic Stars. II

Numerous indications that the magnetic field structures in magnetic stars do not change with age are cited. The stars rotate like a solid.

Signatures of Strangeness in Neutron Star Merger Remnants

Abstract Neutron star (NS) mergers provide us with information rich in physics using multimessenger astrophysical observations. One of the probable remnants of such a merger is a differentially rotating hot hypermassive NS. The stability of the merger remnant crucially depends on the underlying equation of state and thus provides a method to probe the nature of dense matter in NSs. In this work, we search for possible signatures of strangeness-containing matter in NS interiors on the secular stability of the merger remnant. We also use recently proposed methods to make a rough estimate of the collapse time of the merger remnant and the threshold mass above which the merger promptly collapses to a black hole.

Reducing geogenic arsenic leaching from excavated sedimentary soil using zero-valent iron amendment followed by dry magnetic separation: A case study

Although the deep-layer sedimentary soils excavated from construction sites contain low level of geogenic arsenic (As), remediation is necessary when the As leachability exceeds the environmental standard (10 μg/L) in Japan. In this study, the zero-valent iron (ZVI) amendment followed by dry magnetic separation (ZVI-DMS) was implemented for the treatment of a geogenic As-contaminated alkaline sedimentary soil (pH 8.9; 7.5 mg/kg of total As; 0.33 mg/kg of water-extractable As). This technology involves pH adjustment (adding H2SO4), ZVI addition, water content reduction (adding water adsorbent CaSO4·0.5H2O), and dry magnetic separation. The short-term and long-term As leachability before and after treatment was compared using sequential water leaching tests (SWLT). The results illustrated that As could be removed from the bulk soil through the magnetic separation of As-ZVI complexes, although the amount was limited (about 2% of total As). Moreover, immobilization played a dominant role in suppressing As leaching. The H2SO4 addition decreased pH to a circumneutral range and thereby suppress As release. The CaSO4·0.5H2O addition also contributed to the pH decrease and reduced As leachability. Besides, CaSO4·0.5H2O-dissolution released Ca2+ that favored As adsorption, and enhanced dissolved organic carbon (DOC) coagulation that decelerated As dissolution. SWLT results indicated that As leachability from remediated soil satisfied the environmental standard (10 μg/L) in both short-term and long-term perspective. However, the secular stability of treated soil deserves more attention due to the easy re-release of As caused by As-bearing framboidal pyrite oxidation. Additionally, during ZVI-DMS process, there is a need to scientifically decide the dosage of ZVI to avoid excessive addition. Our results demonstrated that ZVI-DMS technology could be a promising remediation strategy for geogenic As contaminated sedimentary soils/rocks.

Secular Stability of Magnetic Field Structures in Magnetic CP-Stars

The magnetic field structures of stars with different ages are studied. No changes in the position and orientation of magnetic dipoles with age are observed. It is concluded that there are no global motions, such as differential rotation meridional circulation, etc., inside magnetic stars. Arguments are presented in favor of the assumption that magnetic stars rotate as solids. These conclusions do not concern the behavior of convective cores.

Stability of planets in triple star systems

Context. Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been for coplanar orbits and with a limited number of orbital parameters. Aims. Our objective is to provide a more generalized empirical mapping of the regions of planetary stability in triples by considering both prograde and retrograde motion of planets and the outer star; investigating highly inclined orbits of the outer star; extending the parameters used to all relevant orbital elements of the triple’s stars and expanding these elements and mass ratios to wider ranges that will accommodate recent and possibly future observational discoveries. Methods. Using N-body simulations, we integrated numerically the various four-body configurations over the parameter space, using a symplectic integrator designed specifically for the integration of hierarchical multiple stellar systems. The triples were then reduced to binaries and the integrations repeated to highlight the differences between these two types of system. Results. This established the regions of secular stability and resulted in 24 semi-empirical models describing the stability bounds for planets in each type of triple orbital configuration. The results were then compared with the observational extremes discovered to date to identify regions that may contain undiscovered planets.

Problems of Hydrodynamics for a Triaxial Ellipsoid

Problems of motion of a triaxial ellipsoid in an ideal liquid and in a viscous liquid in the Stokes approximation and also equilibrium shapes of the rotating gravitating liquid mass are considered. Solutions of these problems expressed via four quadratures depending on four parameters are significantly simplified because they are expressed via the only function of two arguments. The efficiency of the proposed approach is demonstrated by means of analyzing the velocity and pressure fields in an ideal liquid, calculating the added mass of the ellipsoid, determining the viscous friction, and studying the equilibrium shapes and stability of the rotating gravitating capillary liquid. The pressure on the triaxial ellipsoid surface is expressed via the projection of the normal to the impinging flow velocity. The shape of an ellipsoid that ensures the minimum viscous drag at a constant volume is determined analytically. A simple equation in elementary functions is derived for determining the boundary of the domains of the secular stability of the Maclaurin ellipsoids. An approximate solution of the problem of equilibrium and stability of a rotating droplet is presented in elementary functions. A bifurcation point with non-axisymmetric equilibrium shapes branching from this point is found.

Probable Inner Magnetic Structures of Magnetic Stars. I

Abstract—The features of the simplest inner structures of a magnetic field, the central dipole and the shifted dipole, are considered. Their secular stability, solidity of rotation, and a great variety of orientations of magnetic dipoles and magnitudes of magnetic fields are noted.

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov–Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (∼120°), beyond which the agreement is marginal. At such high inclinations, the stability radius is larger, the ratio between the outer and inner periods becomes comparable and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non-co-planar systems, our results have direct implications for any triple systems and, in particular, binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.

Friedman, Chicago, and Monetary Rules

We discuss the development of policy rules at the University of Chicago and compare those rules with modern, Taylor-type rules. A key feature of the 1930s Chicago approach was the view that discretionary monetary policy has a destabilizing effect on the economy. Empirical confirmation of this view was provided by Friedman and Schwartz during the 1950s. Friedman’s empirical findings that: (1i) the money supply can be controlled by the monetary authorities; and (ii2) the demand for money exhibits secular stability, provided the underpinnings for his money-supply rule. Friedman’s statistical approach led him to believe that relationships formed on the basis of structural-parameter estimates within the cycle were likely to be unreliable. Both the Friedman rule and the Taylor rule share several important characteristics, including the focus on reducing both policy uncertainty and the possibility of reducing the policy mistakes of the past. We argue, however, that am implicit aspect of modern rules may pave the way for a return to discretion.

STABILITY OF RIGIDLY ROTATING SUPERMASSIVE STARS AGAINST GRAVITATIONAL COLLAPSE

ABSTRACT We revisit secular stability against quasi-radial collapse for rigidly rotating supermassive stars (SMSs) in general relativity. We suppose that the SMSs are in a nuclear-burning phase and can be modeled by polytropic equations of state with the polytropic index n p slightly smaller than 3. The stability is determined in terms of the turning point method. We find a fitting formula of the stability condition for the plausible range of n p ( 2.95 &lsim; n p &lsim; 3 ?> ) for SMSs. This condition reconfirms that while non-rotating SMSs with a mass of &sim; 10 5 M &CircleDot; ?> – 10 6 M &CircleDot; ?> may undergo a general relativistically induced quasi-radial collapse, rigidly rotating SMSs with a ratio of rotational to gravitational potential energy (β) of &sim; 10 &minus; 2 ?> are likely to be stable against collapse unless they are able to accrete ∼5 times more mass during the (relatively brief) hydrogen-burning phase of their evolution. We discuss the implications of our results.

The isotopic composition of authigenic chromium in anoxic marine sediments: A case study from the Cariaco Basin

Chromium (Cr) isotopes are an emerging proxy for tracking redox processes at the Earth's surface. However, there has been limited exploration of the Cr isotope record of modern and recent marine sediments. The basic inorganic chemistry of Cr suggests that anoxic marine basins should factor prominently in the global Cr cycle and that sediments deposited within anoxic basins may offer a valuable Cr isotope archive throughout Earth's history. Here, we present δ53Cr data from sediments of the Cariaco Basin, Venezuela—a ‘type’ environment for large, perennially anoxic basins with a relatively strong hydrological connection to the global oceans. We document a marked positive shift in bulk δ53Cr values following the termination of the Last Glacial Maximum, followed by relative stasis. Based on a suite of independent redox proxies, this transition marks a switch from oxic to persistently anoxic and sulfidic (euxinic) depositional conditions within the basin. We find good agreement between two independent approaches toward estimating the δ53Cr composition of authigenic Cr in euxinic Cariaco Basin sediments and that these estimates are very similar to the δ53Cr composition of modern open Atlantic Ocean seawater. These data, together with considerations of reaction kinetics and mass balance within the Cariaco Basin, are consistent with the hypothesis that anoxic marine settings can serve as a chemical archive of first-order trends in seawater δ53Cr composition. Additionally, the Cariaco Basin data suggest that there has been secular stability in the average δ53Cr value of Atlantic seawater over the last ∼15 kyr.

Propriedades Psicométricas do Inventário de Depressão de Beck-II (BDI-II) em Uma Amostra Universitária

The objective was to analyze the psychometric properties of the BDI-II to make the construct validity of the inventory, beyond observing associated factors to the depressive symptomatology, its correlation and significance degrees. The sample was composed by 857 university students of a particular university from the State of Rio Grande do Sul. A socio-demographic data questionnaire and the BDI-II were used. The statistical analysis were made by keeping a level of significance of 5%. The results had been: Cronbach’s alpha of 0,89; there were verified a good secular stability (ri = 0,73; p < 0,001); by methods of factor analysis, the items are reduced to three factors that explain 44,57% of total variation. It was observed that 8.8% of the sample presented depressive symptoms. Moreover, correlations of depressive symptoms with some associated factors are presented.