Dynamical complexity of Anosov systems driven by a quasi-periodic force

Consider C^(2)Anosov systems on a compact manifold driven by a quasi-periodic force.We study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic processes.Assuming that these systems are non-wandering(i.e.,every point in the phase space is nonwandering),we prove a set of results:(1)the existence of abundance of random periodic points;(2)a random Livsic theorem;(3)a random Mañé-Bousch-Conze-Guivarc'h lemma;(4)the existence of strong random horseshoes.Additionally,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.

Quasi-periodic orbits of small solar sails with time-varying attitude around Earth–Moon libration points

This paper proposes new quasi-periodic orbits around Earth–Moon collinear libration points using solar sails.By including the time-varying sail orientation in the linearized equations of motion for the circular restricted three-body problem(CR3BP),four types of quasi-periodic orbits(two types around L1 and two types around L2)were formulated.Among them,one type of orbit around L2 realizes a considerably small geometry variation while ensuring visibility from the Earth if(and only if)the sail acceleration due to solar radiation pressure is approximately of a certain magnitude,which is much smaller than that assumed in several previous studies.This means that only small solar sails can remain in the vicinity of L2 for a long time without propellant consumption.The orbits designed in the linearized CR3BP can be translated into nonlinear CR3BP and high-fidelity ephemeris models without losing geometrical characteristics.In this study,new quasi-periodic orbits are formulated,and their characteristics are discussed.Furthermore,their extendibility to higher-fidelity dynamic models was verified using numerical examples.

Autonomous navigation to quasi-periodic orbits near translunar libration points

Libration-point missions have been very useful and successful. Due to the unstable natures of most of these orbits, the long-time stationkeeping demands frequent maneuvers and precise orbit determinations. Earth-based tracking will have to undertake much more responsibilities with the increasing number of libration missions. An autonomous navigation system could offer a better way to decrease the need for Earth-based tracking. Nevertheless, when an autonomous navigation system is applied, there are three important factors affecting autonomous navigation accuracy, i.e., the accuracy of initial conditions, the accuracy of measurements, and the accuracy of onboard dynamics for propagation. This paper focuses on analyzing the influence from the third factor and finding an appropriate navigation dynamics, which can satisfy the requirement of estimation accuracy but not cause too much burden for onboard computation. When considering the restricted three-body model and the bicircular restricted four-body model as navigation dynamics, the astrin- gency is not shown during the simulations. Meanwhile, when considering the influences of the Sun＇s direct and indirect perturbations and the eccentricity of the Moon＇s orbit, a new navigation dynamic model with the standard ephemerides is proposed. The simulation shows the feasibility of the proposed model.

Leveraging quasi-periodic orbits for trajectory design in cislunar space

Incorporating quasi-periodic orbits into the preliminary design process offers a wide range of options to meet mission constraints and address the challenges in a complex trade space.In this investigation,linear stability and quasi-periodic orbit family continuation schemes are examined to meet various types of constraints.Applications in eclipse avoidance and transfer design are examined by leveraging quasi-periodic orbits and their associated hyperbolic manifolds in the lunar region.Solutions are transitioned to an ephemeris model to validate that geometries are maintained in higher-fidelity models.When the natural dynamical structures associated with quasi-periodic orbits are leveraged,novel trajectory solutions can emerge.

Research on the flow stability and noise reduction characteristics of quasi-periodic elastic support skin

To enhance flow stability and reduce hydrodynamic noise caused by fluctuating pressure,a quasiperiodic elastic support skin composed of flexible walls and elastic support elements is proposed for fluid noise reduction.The arrangement of the elastic support element is determined by the equivalent periodic distance and quasi-periodic coefficient.In this paper,a dynamic model of skin in a fluid environment is established.The influence of equivalent periodic distance and quasi-periodic coefficient on flow stability is investigated.The results suggest that arranging the elastic support elements in accordance with the quasi-periodic law can effectively enhance flow stability.Meanwhile,the hydrodynamic noise calculation results demonstrate that the skin exhibits excellent noise reduction performance,with reductions of 10 dB in the streamwise direction,11 dB in the spanwise direction,and 10 dB in the normal direction.The results also demonstrate that the stability analysis method can serve as a diagnostic tool for flow fields and guide the design of noise reduction structures.

人工智能助力:Orbital Materials公司加速清洁技术材料的开发

随着全球对环境保护意识的增强,探寻能够有效减少碳排放并促进可持续发展的新材料成为了科研领域的热点。一家成立于2022年的初创公司Orbital Materials,正利用人工智能(AI)技术在这一领域取得突破。

Effect of orbital symmetry on atomic ionization in near-infrared laser fields

We have performed a comparative study of the photoelectron spectra adopting different initial states(2s or 2_(p0))of hydrogen atoms in a near-infrared laser pulse by using the full three-dimensional time-dependent Schr?dinger equation.It is demonstrated that the atomic photoelectron spectra oscillate out of step as a function of electron kinetic energies for different initial states(2s or 2_(p0)),which is well reproduced by the simulations based on strong field approximation,and the above distinct feature is ascribed to the different interferences from the partial electron wave packets detached by positive and negative electric fields for different initial states of 2s and 2_(p0).

Guidelines for standard operation of imaging modalities in orbital diseases (2024)

Orbital disorders include conditions originating from the orbital bones,surrounding tissues,and post-orbital septum.They also include systemic ailments affecting the orbit.Different clinical symptoms make up the complex range of orbital disorders.Because these disorders mostly impact the orbital area instead of the intraocular compartment,there is little diagnostic usefulness for typical ophthalmic visual tests.As such,the vital instruments for diagnosing and evaluating orbital illnesses have become ophthalmic imaging modalities,including ocular ultrasonography(B-scan),computed tomography(CT),and magnetic resonance imaging(MRI).One way to improve the precision and promptness of diagnosing orbital diseases is to standardize the functioning of widely used imaging equipment and define the radiological features of orbital abnormalities.Such programs are crucial for the care of patients with orbital disorders since they considerably reduce the number of misdiagnoses and missed diagnoses in these individuals.The underlying concepts,operational techniques,and normal and pathological imaging findings associated with common diagnostic tools for orbital illnesses are all thoroughly reviewed in this guideline.The objective is to improve primary healthcare settings’diagnostic competence in the field of orbital pathology and to standardize procedures for diagnosing orbital disorders.

Impulsive thrust strategy for orbital pursuit-evasion games based on impulse-like constraint

This paper proposes a novel impulsive thrust strategy guided by optimal continuous thrust strategy to address two-player orbital pursuit-evasion game under impulsive thrust control.The strategy seeks to enhance the interpretability of impulsive thrust strategy by integrating it within the framework of differential game in traditional continuous systems.First,this paper introduces an impulse-like constraint,with periodical changes in thrust amplitude,to characterize the impulsive thrust control.Then,the game with the impulse-like constraint is converted into the two-point boundary value problem,which is solved by the combined shooting and deep learning method proposed in this paper.Deep learning and numerical optimization are employed to obtain the guesses for unknown terminal adjoint variables and the game terminal time.Subsequently,the accurate values are solved by the shooting method to yield the optimal continuous thrust strategy with the impulse-like constraint.Finally,the shooting method is iteratively employed at each impulse decision moment to derive the impulsive thrust strategy guided by the optimal continuous thrust strategy.Numerical examples demonstrate the convergence of the combined shooting and deep learning method,even if the strongly nonlinear impulse-like constraint is introduced.The effect of the impulsive thrust strategy guided by the optimal continuous thrust strategy is also discussed.

OrbitMI的数字化解决方案

近日,劳氏日报揭晓了2024年度十大科技领袖榜单,OrbitMI公司的首席执行官Ali Riaz以其卓越的领导力成功上榜,位列第6。OrbitMI的前身是被誉为极具创新精神的瑞典油轮公司Stena Bulk的一个部门。Stena Bulk的全球开发团队与海事和能源专家、麻省理工学院的工程师合作,采用创新方法创建了基于实际使用案例的解决方案,建立了名为Orbit的运营平台,旨在提高效率,使公司更加灵活,增加与客户之间的透明度,并加强市场信息收集。很快,Orbit便无缝融入了Stena Bluk的日常工作。

Optimal quasi-periodic maintenance policies for two-unit series system

To investigate the effects of various random factors on the preventive maintenance （PM） decision-making of one type of two-unit series system, an optimal quasi-periodic PM policy is introduced. Assume that PM is perfect for unit 1 and only mechanical service for unit 2 in the model. PM activity is randomly performed according to a dynamic PM plan distributed in each implementation period. A replacement is determined based on the competing results of unplanned and planned replacements. The unplanned replacement is trigged by a catastrophic failure of unit 2, and the planned replacement is executed when the PM number reaches the threshold N. Through modeling and analysis, a solution algorithm for an optimal implementation period and the PM number is given, and optimal process and parametric sensitivity are provided by a numerical example. Results show that the implementation period should be decreased as soon as possible under the condition of meeting the needs of practice, which can increase mean operating time and decrease the long-run cost rate.

On reducibility of a class of nonlinear quasi-periodic systems with small perturbational parameters near equilibrium

Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system x = （A ＋ εQ（ t） ）x ＋ eg（t） ＋ h（x, t）, where A is a constant matrix with multiple eigenvalues; h = O（x2） （x-4）） ; and h（x, t）, Q（t）, and g（t） are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

Quasi-Periodic Waves and Asymptotic Property for Boiti-Leon-Manna-Pempinelli Equation

In this paper,multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli(BLMP) equation by using Hirota bilinear method and Riemann theta function.At the same time,weanalyze in details asymptotic properties of the multi-periodic wave solutions and give their asymptotic relations betweenthe periodic wave solutions and the soliton solutions.

CHARACTERISTICS OF QUASI-PERIODIC OSCILLATIONS DURING SEA FOG EVENTS

Based on the high-resolution datasets collected in a sea fog field experiment at the northern coast of South China Sea,the variations of liquid water content (LWC) and net longwave radiation flux (NLRF) during two sea fog events on 16th-17th and 18th-19th March,2008 are exaimeed by wavelet analysis,and the cooling mechanisms for fog formation and persistence are also investigated.The main results are shown as follows.(1) Sea fog may develop and persist whether it is cloudy or not aloft.However,when there is cloud aloft the LWC is less and wind speed in sea fog is higher than that in the clear sky.(2) The quasi-periodic oscillations (QPOs) of NLRF are observed in the formation stage of the two fogs.QPOs of LWC are only found in the developing stage no matter with cloudless or cloudy condition.(3) It is likely that sea fog forms by the cooling effects of longwave radiation and develops through the vertical mixing induced by the radiative cooling at the upper level.(4) During sea fog development and persistence,other mechanisms could also play important roles in fog-layer cooling,such as turbulent heat transport and radiation transport between air-sea interfaces.

Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. Here in this paper, we will present effective and accurate algorithms for quasi-periodic solutions by improving Wilson-θ and Newmark-β methods, respectively. In both the two methods, routinely, the considered equations are rearranged in the form of incremental equilibrium equations with the coefficient matrixes being updated in each time step. In this study, the two methods are improved via a predictor-corrector algorithm without updating the coefficient matrixes, in which the predicted solution at one time point can be corrected to the true one at the next. Numerical examples show that, both the improved Wilson-θ and Newmark-β methods can provide much more accurate quasi-periodic solutions with a smaller amount of computational resources. With a simple way to adjust the convergence of the iterations, the improved methods can even solve some quasi-periodic systems effectively, for which the original methods cease to be valid.

Geometric Aspects of Quasi-Periodic Property of Dirichlet Functions

The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value taken by it at any point belonging to that line and a bounded domain Ω. He proved that the functions defined by ordinary Dirichlet series are quasi-periodic in their half plane of uniform convergence. We realized that the existence of the domain Ω is not necessary and that the quasi-periodicity is related to the denseness property of those functions which we have studied in a previous paper. Hence, the purpose of our research was to prove these two facts. We succeeded to fulfill this task and more. Namely, we dealt with the quasi-periodicity of general Dirichlet series by using geometric tools perfected by us in a series of previous projects. The concept has been applied to the whole complex plane (not only to the half plane of uniform convergence) for series which can be continued to meromorphic functions in that plane. The question arise: in what conditions such a continuation is possible? There are known examples of Dirichlet series which cannot be continued across the convergence line, yet there are no simple conditions under which such a continuation is possible. We succeeded to find a very natural one.

Studies of Optical Properties of Symmetrical Quasi-Periodic Photonic Crystals

Using the transfer matrix method approach (TMM), the present paper attempts to determine the optical properties of quasi-periodic symmetric one-dimensional photonic systems. In addition, it studies hybrid hetero-structure systems constructed by using periodic and quasi-periodic multilayer systems. The effect of symmetry applied to symmetric multilayer systems results in the appearance of optical windows at the photonic band gaps (PBG) of the system. The use of hybrid symmetric systems, at normal incidence in the visible range, show that the complete photonic band gap is the sum of bands from individual systems. The results show also that the width of the PBG depends on the parameters and nature of the built system.

Quasi-periodic events on structured earthquake models

There has been much interest in studying quasi-periodic events on earthquake models.Here we investigate quasiperiodic events in the avalanche time series on structured earthquake models by the analysis of the autocorrelation function and the fast Fourier transform.For random spatial earthquake models, quasi-periodic events are robust and we obtain a simple rule for a period that is proportional to the choice of unit time and the dissipation of the system.Moreover, computer simulations validate this rule for two-dimensional lattice models and cycle graphs, but our simulation results also show that small-world models, scale-free models, and random rule graphs do not have periodic phenomena.Although the periodicity of avalanche does not depend on the criticality of the system or the average degree of the system or the size of the system,there is evidence that it depends on the time series of the average force of the system.

ORBIT评分与HAS-BLED评分对心脏瓣膜置换术后华法林抗凝出血风险的预测价值比较

目的比较ORBIT评分与HAS-BLED评分对心脏瓣膜置换术后华法林抗凝出血风险的预测价值。方法回顾性分析304例心脏瓣膜置换术后需行华法林抗凝治疗患者的病例资料,分别根据ORBIT评分和HAS-BLED评分对患者进行风险分层和分组,分析基于不同评分的风险分层与术后华法林抗凝出血事件的相关性,比较2种评分方法风险分层的一致性及其对出血事件的预测价值。结果304例患者中,出血患者32例、未出血患者272例,出血患者的术后ORBIT评分、HAS-BLED评分均高于未出血患者,差异有统计学意义(P<0.05)。基于ORBIT评分划分的中危、高危患者的出血风险分别为低危患者的6.092(95%CI:2.694~13.775)倍、9.373(95%CI:1.465~59.943)倍,基于HAS-BLED评分划分的中危、高危患者的出血风险分别为低危患者的3.750(95%CI:1.383~10.166)倍、14.250(95%CI:5.489~36.995)倍。受试者工作特征曲线分析结果显示,ORBIT评分预测华法林抗凝出血风险的曲线下面积(AUC)为0.646(95%CI:0.589~0.699),敏感度为46.88%,特异度为87.87%,最佳截断值为3分;HAS-BLED评分预测华法林抗凝出血风险的AUC为0.768(95%CI:0.717~0.814),敏感度为75.00%,特异度为69.85%,最佳截断值为2分;Delong检验结果显示,2种评分的AUC差异有统计学意义(D=0.122,95%CI:0.001~0.245,Z=1.962,P<0.05)。结论ORBIT评分和HAS-BLED评分对心脏瓣膜置换术后华法林抗凝出血风险均具有一定预测价值,其中HAS-BLED评分的预测效能更优。