Stability and Motion around Equilibrium Points in the Rotating Plane-Symmetric Potential Field

This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by the structure of the submanifolds and subspaces. The non-degenerate equilibrium points are classified into twelve cases. The necessary and sufficient conditions for linearly stable, non resonant unstable and resonant equilibrium points are established. Furthermore, the results show that a resonant equilibrium point is a Hopf bifurcation point. In addition, if the rotating speed changes, two non degenerate equilibria may collide and annihilate each other. The theory developed here is lastly applied to two particular cases, motions around a rotating, homogeneous cube and the asteroid 1620 Geographos. We found that the mutual annihilation of equilibrium points occurs as the rotating speed increases, and then the first surface shedding begins near the intersection point of the x axis and the surface. The results can be applied to planetary science, including the birth and evolution of the minor bodies in the Solar system, the rotational breakup and surface mass shedding of asteroids, etc.Comment: 38 pages, 7 figures. arXiv admin note: text overlap with arXiv:1403.040

Monte Carlo Analysis for Significant Parameters Ranking in RLV Flight Evaluation

AbstractMonte Carlo simulation is an effectivemethod for evaluating complex systems. Besides estimating the performancelevel of the system through Monte Carlo method, it is more wanted to identifykey factors in system operation so as to improve or redesign the system. When estimating the performance level, in order to obtainsufficientevaluation accuracy while keeping time cost as low as possible, its relation with confidence leveland number of simulation runs is explained according to probability and statistics theory. To identify key factors, a method ranking the significant influencing parameters automaticallyfor complex systemsbased on naive Bayes classifier (NBC) and kernel density estimator (KDE) is developed. NBC used for classification makes the method valid for all kinds of linear and nonlinear complex systems, and KDE contributes greatly to identifyingsignificant influencing parameters in automated manner.The method above is applied toa reusable launch vehicle (RLV) flight evaluation.Through the evaluation, bias of atmosphere density is identified as the most significant parameter which relies on the flight control mode in the terminal flight phase

Time-optimal formation establishment around a slowly rotating asteroid

A study is conducted to find a solution to the problem of time-optimal formation establishment around a slowly rotating asteroid, whose gravity is approximated as a second-degree and second-order gravitational field (SDSOGF). Similar to the methodology used for identifying the classical J2-invariant relative orbits, two necessary conditions are analytically derived to guarantee bounded relative motion in an SDSOGF. In particular, it is shown that when the nonspherical harmonic coefficients of the asteroid gravity are first-order small, the resulting necessary conditions are consistent with the recent literature results. Based on the analytically obtained constraints, the problem of time-optimal formation establishment is then emphasized via an indirect approach, in which the initial unknown costate vector is calculated with a scaling technique to alleviate its sensitivity to the initial guess problem

Schmeissneria: A missing link to angiosperms?

BACKGROUND: The origin of angiosperms has been under debate since the time of Darwin. While there has been much speculation in past decades about pre-Cretaceous angiosperms, including Archaefructus, these reports are controversial. The earliest reliable fossil record of angiosperms remains restricted to the Cretaceous, even though recent molecular phylogenetic studies suggest an origin for angiosperms much earlier than the current fossil record. RESULTS: In this paper, after careful SEM and light microscopic work, we report fossils with angiospermous traits of the Jurassic age. The fossils were collected from the Haifanggou Formation (middle Jurassic) in western Liaoning, northeast China. They include two female structures and an associated leaf on the same slab. One of the female structures is physically connected to the apex of a short shoot. The female organs are borne in pairs on short peduncles that are arranged along the axis of the female structure. Each of the female organs has a central unit that is surrounded by an envelope with characteristic longitudinal ribs. Each central unit has two locules completely separated by a vertical septum. The apex of the central unit is completely closed. The general morphology places these fossils into the scope of Schmeissneria, an early Jurassic genus that was previously attributed to Ginkgoales. CONCLUSION: Because the closed carpel is a character only found in angiosperms, the closed apex of the central unit suggests the presence of angiospermy in Schmeissneria. This angiospermous trait implies either a Jurassic angiosperm or a new seed plant group parallel to angiosperms and other known seed plants. As an angiosperm, the Liassic age (earliest Jurassic) of Schmeissneria microstachys would suggest an origin of angiosperms during the Triassic. Although still uncertain, this could have a great impact on our perspective of the history, diversity and systematics of seed plants and angiosperms

Effect of Family Nutrition Therapy on Elderly Patients with Chronic Obstructive Pulmonary Disease

Objective: The aim of the study was to explore the influence of family enteral nutrition support on nutritional status, lung function, activity tolerance and quality of life in elderly patients with chronic obstructive pulmonary disease (COPD) in stable stage and malnutrition. Methods: A prospective observational study of COPD and malnutrition in the geriatric department of our hospital, control group (n=82) and intervention group n=82). The control group was treated with conventional diet, and the intervention group was treated with conventional diet and enteral nutrition suspension. One month later, observe the nutrition indicators,lung function,exercise tolerance and quality of life. Results: (1) BMI and ALB were higher than control group (t = 10.465, 6.189, P 0.05). (2) FVC, FEV1, FEV1 / FVC, FEV1% were higher than control group (t = 11.999, 19.654, 13.418, 16.924, P < 0.05). (3) the quality of life symptom score, activity score, influence score and total score were lower than control group (t = 15.303, 6.773, 23.600, 14.766, P < 0.05), and 6MWT were higher than control group (t = 111.962, P < 0.05). Conclusion:Oral enteral nutritioncan improve the nutritional status, lung function, activity tolerance and quality of life of elderly patients with COPD in stable stage and malnutrition.It can be a early,safe and effective nutritional support strategy for COPD patients with malnutritio

Survival and risk factors associated with surgical repair of ventricular septal rupture after acute myocardial infarction: A single-center experience

ObjectiveTo analyze the survival and risk factors associated with the surgical treatment of ventricular septal rupture (VSR) after acute myocardial infarction (AMI).MethodsWe retrospectively analyzed 45 consecutive patients with VSR after AMI whose procedures were performed in the Department of Cardiovascular Surgery at the General Hospital of Northern Theater Command between January 2012 and December 2021. Relevant clinical data, surgery-related conditions, and follow-up data of all patients were summarized. Patients were divided into the survival group and the death group. The Kaplan–Meier method and log-rank test were used to determine the cumulative incidence of all-cause mortality. Multivariate logistic regression was used to evaluate the independent risk factors for all-cause mortality.ResultsThe average postoperative follow-up time was 42.1 ± 34.1 months. The overall mortality rate was 20% (9/45 patients) and the operative mortality rate was 8.9% (4/45 patients). Logistic analysis showed that the death group had higher serum creatinine (127.32 ± 47.82 vs. 82.61 ± 27.80 μmol/L, respectively; P = 0.0238) and N-terminal pro-B-type natriuretic peptide (NT-proBNP) [8,654.00 pg/mL (6,197.00–11,949.00 pg/mL) vs. 4,268.96 pg/mL (1,800.00–7,894.00 pg/mL), respectively; P = 0.0134] levels than the survival group. The cardiopulmonary bypass time (CPB) was longer in the death group than in the survival group [131.00 min (121.00–184.00 min) vs. 119.00 min (103.00–151.50 min), respectively; P = 0.0454]. Significantly more red blood cells were transfused in the death group than in the survival group [11.60 units (6.10–16.50) vs. 3.75 units (0.00–7.00 units), respectively; P = 0.0025]. Intra-aortic balloon pump (IABP) implantation (P = 0.016) and ventilation time (P = 0.0022) were risk factors for mortality. A 1-month landmark analysis showed that compared with patients with VSR to surgical time &gt;14 days, patients who underwent surgery within 14 days had a higher rate of all-cause mortality (25.00 vs. 3.33%; log-rank P = 0.023). Patients with VSR within 14 days also had a higher rate of residual shunts that were higher than moderate. Multivariate analysis showed that transfusion of red blood cells and NT-proBNP level were risk factors for all-cause mortality, as well as major adverse cardiovascular and cerebrovascular events.ConclusionsSurgical repair resulted in good outcomes for patients with VSR after AMI. Patients with VSR to surgical time &gt;14 days had a lower rate of all-cause mortality. Treatment strategies for VSR should be based on the patient's condition and comprehensively determined through real-time evaluation and monitoring

The danger of mapping risk from multiple natural hazards

In recent decades, society has been greatly affected by natural disasters (e.g. floods, droughts, earthquakes), losses and effects caused by these disasters have been increasing. Conventionally, risk assessment focuses on individual hazards, but the importance of addressing multiple hazards is now recognised. Two approaches exist to assess risk from multiple-hazards; the risk index (addressing hazards, and the exposure and vulnerability of people or property at risk) and the mathematical statistics method (which integrates observations of past losses attributed to each hazard type). These approaches have not previously been compared. Our application of both to China clearly illustrates their inconsistency. For example, from 31 Chinese provinces assessed for multi-hazard risk, Gansu and Sichuan provinces are at low risk of life loss with the risk index approach, but high risk using the mathematical statistics approach. Similarly, Tibet is identified as being at almost the highest risk of economic loss using the risk index, but lowest risk under the mathematical statistics approach. Such inconsistency should be recognised if risk is to be managed effectively, whilst the practice of multi-hazard risk assessment needs to incorporate the relative advantages of both approaches

Time-Optimal Spacecraft Reorientation for the Observation of Multiple Asteroids

To observe multiple asteroids in a short time, the time-optimal reorientation is investigated here for the rest-to-rest reorientation of a generic rigid spacecraft. First, the problem is formulated and solved using the hp-adaptive pseudospectral method. It is found that there exist not merely bang-bang but also singular solutions for the problem. Then, the bang-bang and singular solutions are discussed by various cases. The results reveal that the optimal solution is essentially a balance between the larger torque, the shorter angular path and the less moment of inertia. For bang-bang solutions, the total number of switches varies with the reorientation angle and the moment of inertia. The number of switches is usually 5 or 6 and does not exceed 8. For singular solutions, either one and two controls singular are possible. The singular optimal solution is probably optimal for the slender rod-like spacecraft. Finally, an analytical estimation method is proposed for determining the range of the optimal time. The results of the simulations indicate that the proposed method is real-time and highly accurate. All formulas of this paper are derived in canonical units and therefore apply to any rigid spacecraft