In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadra...In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadratic and quadratic behaviors simultaneously in different variable components.展开更多
It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cy...It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.展开更多
Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Dear Editor,Idiopathic orbital inflammation(IOI),also known as orbital inflammatory pseudotumor,is a relatively common orbital disorder[1].Its pathogenesis remains unclear,often regarded as a nonspecific immune-mediat...Dear Editor,Idiopathic orbital inflammation(IOI),also known as orbital inflammatory pseudotumor,is a relatively common orbital disorder[1].Its pathogenesis remains unclear,often regarded as a nonspecific immune-mediated response[2].IOI presents with symptoms such as pain,photophobia,proptosis,eyelid swelling,edema,conjunctival congestion,and diplopia,with possible vision loss occurring in some cases.Based on the soft tissue structures involved,IOI can be classified into subtypes such as myositis,optic neuritis,dacryoadenitis,diffuse orbital inflammation,and orbital inflammatory masses[2].展开更多
In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dime...In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimensional continuous maps with certain specific periodic points.Further, we obtain results for the existence of chaotic phenomenon in the sense of Li and Yorke. Some examples are also analyzed using the proposed methods.展开更多
AIM:To investigate the clinical features and prognosis of patients with orbital inflammatory myofibroblastic tumor(IMT).METHODS:This retrospective study collected clinical data from 22 patients diagnosed with orbital ...AIM:To investigate the clinical features and prognosis of patients with orbital inflammatory myofibroblastic tumor(IMT).METHODS:This retrospective study collected clinical data from 22 patients diagnosed with orbital IMT based on histopathological examination.The patients were followed up to assess their prognosis.Clinical data from patients,including age,gender,course of disease,past medical history,primary symptoms,ophthalmologic examination findings,general condition,as well as imaging,laboratory,histopathological,and immunohistochemical results from digital records were collected.Orbital magnetic resonance imaging(MRI)and(or)computed tomography(CT)scans were performed to assess bone destruction of the mass,invasion of surrounding tissues,and any inflammatory changes in periorbital areas.RESULTS:The mean age of patients with orbital IMT was 28.24±3.30y,with a male-to-female ratio of 1.2:1.Main clinical manifestations were proptosis,blurred vision,palpable mass,and pain.Bone destruction and surrounding tissue invasion occurred in 72.73%and 54.55%of cases,respectively.Inflammatory changes in the periorbital site were observed in 77.27%of the patients.Hematoxylin and eosin staining showed proliferation of fibroblasts and myofibroblasts,accompanied by infiltration of lymphocytes and plasma cells.Immunohistochemical staining revealed that smooth muscle actin(SMA)and vimentin were positive in 100%of cases,while anaplastic lymphoma kinase(ALK)showed positivity in 47.37%.The recurrence rate of orbital IMT was 27.27%,and sarcomatous degeneration could occur.There were no significant correlations between recurrence and factors such as age,gender,laterality,duration of the disease,periorbital tissue invasion,bone destruction,periorbital inflammation,tumor size,fever,leukocytosis,or treatment(P>0.05).However,lymphadenopathy and a Ki-67 index of 10%or higher may be risk factors for recurrence(P=0.046;P=0.023).CONCLUSION:Orbital IMT is a locally invasive disease that may recur or lead to sarcomatoid degeneration,primarily affecting young and middle-aged patients.The presence of lymphadenopathy and a Ki-67 index of 10%or higher may signify a poor prognosis.展开更多
AIM:To define the prevalence and anatomical patterns of paranasal sinus abnormalities(PSA)in thyroid-associated ophthalmopathy(TAO)and to test the hypothesis that TAO is partially driven by contiguous orbital inflamma...AIM:To define the prevalence and anatomical patterns of paranasal sinus abnormalities(PSA)in thyroid-associated ophthalmopathy(TAO)and to test the hypothesis that TAO is partially driven by contiguous orbital inflammation rather than systemic autoimmunity or generalized orbital pressure.METHODS:Data included ophthalmic assessments and a panel of thyroid function and autoimmune biomarkers.Blinded radiological analysis of orbital computed tomography(CT)scans was performed to quantify sinus abnormalities and extraocular muscles(EOMs)involvement.Patients were categorized into two groups based on CT findings,those with no radiological evidence of sinus abnormalities(non-PSA control group)and those with identifiable PSA.Furthermore,ethmoid sinus mucosal biopsies from a subset of TAO patients and noninflammatory controls were subjected to histopathological analysis.RESULTS:Totally 121 TAO patients(mean age 42.4±12.8y,range 10-78y),male:female=42:79,were included.PSA was identified in 44.6%(n=54)of patients,with a distribution anatomically restricted to the maxillary(50.0%isolated)and ethmoid sinuses(18.5%isolated;29.6%combined).Compared to the non-PSA group(n=67),patients with PSA were significantly older(45.1±11.8 vs 40.3±13.2y;P=0.040)and were more likely to be male(55.6%vs 17.9%;P<0.001).They also had significantly higher proptosis(22.1±3.2 vs 20.7±2.9 mm;P<0.001).Medial/inferior rectus involvement was most frequent(88.4%vs 89.3%).Histopathological analysis of sinus mucosa from PSA patients provided direct evidence of pathology,revealing a dense,chronic lymphoplasmacytic infiltrate and submucosal edema,validating the radiological findings as a true inflammatory process.No significant correlation was found with systemic autoimmune markers,including thyroid-stimulating hormone(TSH)receptor antibodies(TRAb,median 4.86 vs 2.71 IU/L,P=0.104).CONCLUSION:TAO is associated with a high prevalence of PSA in a pattern consistent with the orbital anatomy.The correlation with ipsilateral muscle thickening combined with the lack of association with proptosis laterality or systemic biomarkers lend strong support to a model of contiguous inflammation over systemic autoimmunity,a hypothesis that warrants further validation through longitudinal and mechanistic studies.展开更多
A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not...A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not involve a barrier between patches,further it is assumed that all the parameters are time dependent.It is shown that the system can be made persistent under some appropriate conditions.Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.展开更多
This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential cor...This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.展开更多
This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical...This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model.It focuses the attention on periodic orbits in the Earth-Moon system.This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies.Firstly,simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized,and periodic orbits around Lagrange points,either planar or three-dimensional,are intensively studied during past decades.Subsequently,stability index of a periodic orbit and bifurcation analysis are presented,which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals.Then,the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits,as well as constructing database of periodic orbits by numerical searching techniques are also presented.For those unstable periodic orbits,the station keeping maneuvers are reviewed.Finally,the applications of periodic orbits are presented,including those in practical missions,under consideration,and still in conceptual design stage.This review article has the function of bridging between engineers and researchers,so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem(RTBP).At the same time,it can also provide some technical thinking for general researchers.展开更多
A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consi...A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.展开更多
Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analy...Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.展开更多
The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along hal...The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along halo orbits, a nonlinear output tracking control scheme based on the θ- D technique is proposed. Compared with the popular time-variant linear quadratic regulator （LQR） controller, this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation. Besides, the obtained nonlinear suboptimal controller is in a closed form and easy to implement. Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors. The axis of rotation can keep pointing to an inertial specific object to fulfill an observation mission. In addition, the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.展开更多
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...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.展开更多
In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions betwee...In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.展开更多
The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an e...The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an evolution from periodicity to non-periodicity of the un-captured electron phase orbits after the energy exchange between the electron beam and laser fields.With the increase of the absorbed photon number n by an electron, this evolution will be more and more faster, while it is rapidly decreased with the enhancement of the collision non-flexibility ξ of the electrons and photons; When the electrons are captured by the laser fields, the evolution is finished, the electrons will stably transport,and the photons dont give up the energy to these electrons.展开更多
An improved numerical method that can construct Halo/Lissajous orbits in the vicinity of collinear libration points in a full solar system model is investigated. A full solar system gravitational model in the geocentr...An improved numerical method that can construct Halo/Lissajous orbits in the vicinity of collinear libration points in a full solar system model is investigated. A full solar system gravitational model in the geocentric rotating coordinate system with a clear presentation of the angular velocity relative to the inertial coordinate system is proposed. An alternative way to determine patch points in the multiple shooting method is provided based on a dynamical analysis with Poincare′sections. By employing the new patch points and sequential quadratic programming, Halo orbits for L1, L2, and L3points as well as Lissajous orbits for L1and L2points in the EarthMoon system are generated with the proposed full solar system gravitational model to verify the effectiveness of the proposed method.展开更多
As a classical technique for chaos suppression,the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits(UPOs)embedded in chaotic systems.A critical issue for ach...As a classical technique for chaos suppression,the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits(UPOs)embedded in chaotic systems.A critical issue for achieving high controlling precision is to search for an appropriate time delay.This paper proposes a simple yet effective approach,based on incremental harmonic balance method,to determine the optimal time delay in the delayed feedback controller.The time delay is adjusted within the iterative scheme provided by the proposed method,and finally converges to the period of the target UPO.As long as the optimal time delay is fixed,moreover,the attained solution makes it quite convenient to analyze its stability according to the Floquet theory,which further provides the effective interval of the feedback gain.展开更多
The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neit...The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.展开更多
Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that...Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.展开更多
基金supported by the NSFC(12301138)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(2021L377)+1 种基金the Doctoral Scientific Research Foundation of Shanxi Datong University(2018-B-15)The second author’s work was supported by the NSFC(12171108).
文摘In this paper,the problem of brake orbits with minimal period estimates are considered for the first-order Hamiltonian systems with anisotropic growth,i.e.,the Hamiltonian functions may have super-quadratic,sub-quadratic and quadratic behaviors simultaneously in different variable components.
基金Supported by the National Natural Science Foundation of China(12201446)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(22KJB110005)the Shuangchuang Program of Jiangsu Province(JSSCBS20220898)。
文摘It is known that monotone recurrence relations can induce a class of twist homeomorphisms on the high-dimensional cylinder,which is an extension of the class of monotone twist maps on the annulus or two-dimensional cylinder.By constructing a bounded solution of the monotone recurrence relation,the main conclusion in this paper is acquired:The induced homeomorphism has Birkhoff orbits provided there is a compact forward-invariant set.Therefore,it generalizes Angenent's results in low-dimensional cases.
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
基金Supported by the National Natural Science Foundation of China(No.82388101,No.81930024)the Science and Technology Commission of Shanghai(No.22YS1400400,No.20DZ2270800).
文摘Dear Editor,Idiopathic orbital inflammation(IOI),also known as orbital inflammatory pseudotumor,is a relatively common orbital disorder[1].Its pathogenesis remains unclear,often regarded as a nonspecific immune-mediated response[2].IOI presents with symptoms such as pain,photophobia,proptosis,eyelid swelling,edema,conjunctival congestion,and diplopia,with possible vision loss occurring in some cases.Based on the soft tissue structures involved,IOI can be classified into subtypes such as myositis,optic neuritis,dacryoadenitis,diffuse orbital inflammation,and orbital inflammatory masses[2].
文摘In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimensional continuous maps with certain specific periodic points.Further, we obtain results for the existence of chaotic phenomenon in the sense of Li and Yorke. Some examples are also analyzed using the proposed methods.
基金Supported by the National Key R&D Program of China(No.2023YFC2410203)Beijing Hospitals Authority Clinical Medicine Development of Special Funding Support(No.ZLRK202503).
文摘AIM:To investigate the clinical features and prognosis of patients with orbital inflammatory myofibroblastic tumor(IMT).METHODS:This retrospective study collected clinical data from 22 patients diagnosed with orbital IMT based on histopathological examination.The patients were followed up to assess their prognosis.Clinical data from patients,including age,gender,course of disease,past medical history,primary symptoms,ophthalmologic examination findings,general condition,as well as imaging,laboratory,histopathological,and immunohistochemical results from digital records were collected.Orbital magnetic resonance imaging(MRI)and(or)computed tomography(CT)scans were performed to assess bone destruction of the mass,invasion of surrounding tissues,and any inflammatory changes in periorbital areas.RESULTS:The mean age of patients with orbital IMT was 28.24±3.30y,with a male-to-female ratio of 1.2:1.Main clinical manifestations were proptosis,blurred vision,palpable mass,and pain.Bone destruction and surrounding tissue invasion occurred in 72.73%and 54.55%of cases,respectively.Inflammatory changes in the periorbital site were observed in 77.27%of the patients.Hematoxylin and eosin staining showed proliferation of fibroblasts and myofibroblasts,accompanied by infiltration of lymphocytes and plasma cells.Immunohistochemical staining revealed that smooth muscle actin(SMA)and vimentin were positive in 100%of cases,while anaplastic lymphoma kinase(ALK)showed positivity in 47.37%.The recurrence rate of orbital IMT was 27.27%,and sarcomatous degeneration could occur.There were no significant correlations between recurrence and factors such as age,gender,laterality,duration of the disease,periorbital tissue invasion,bone destruction,periorbital inflammation,tumor size,fever,leukocytosis,or treatment(P>0.05).However,lymphadenopathy and a Ki-67 index of 10%or higher may be risk factors for recurrence(P=0.046;P=0.023).CONCLUSION:Orbital IMT is a locally invasive disease that may recur or lead to sarcomatoid degeneration,primarily affecting young and middle-aged patients.The presence of lymphadenopathy and a Ki-67 index of 10%or higher may signify a poor prognosis.
基金Supported by The National Natural Science Foundation of China(No.82101180)the Fund for Beijing Science&Technology Development of TCM(No.BJZYYB-2023-17)the Beijing Municipal Natural Science Foundation grant(No.7252093).
文摘AIM:To define the prevalence and anatomical patterns of paranasal sinus abnormalities(PSA)in thyroid-associated ophthalmopathy(TAO)and to test the hypothesis that TAO is partially driven by contiguous orbital inflammation rather than systemic autoimmunity or generalized orbital pressure.METHODS:Data included ophthalmic assessments and a panel of thyroid function and autoimmune biomarkers.Blinded radiological analysis of orbital computed tomography(CT)scans was performed to quantify sinus abnormalities and extraocular muscles(EOMs)involvement.Patients were categorized into two groups based on CT findings,those with no radiological evidence of sinus abnormalities(non-PSA control group)and those with identifiable PSA.Furthermore,ethmoid sinus mucosal biopsies from a subset of TAO patients and noninflammatory controls were subjected to histopathological analysis.RESULTS:Totally 121 TAO patients(mean age 42.4±12.8y,range 10-78y),male:female=42:79,were included.PSA was identified in 44.6%(n=54)of patients,with a distribution anatomically restricted to the maxillary(50.0%isolated)and ethmoid sinuses(18.5%isolated;29.6%combined).Compared to the non-PSA group(n=67),patients with PSA were significantly older(45.1±11.8 vs 40.3±13.2y;P=0.040)and were more likely to be male(55.6%vs 17.9%;P<0.001).They also had significantly higher proptosis(22.1±3.2 vs 20.7±2.9 mm;P<0.001).Medial/inferior rectus involvement was most frequent(88.4%vs 89.3%).Histopathological analysis of sinus mucosa from PSA patients provided direct evidence of pathology,revealing a dense,chronic lymphoplasmacytic infiltrate and submucosal edema,validating the radiological findings as a true inflammatory process.No significant correlation was found with systemic autoimmune markers,including thyroid-stimulating hormone(TSH)receptor antibodies(TRAb,median 4.86 vs 2.71 IU/L,P=0.104).CONCLUSION:TAO is associated with a high prevalence of PSA in a pattern consistent with the orbital anatomy.The correlation with ipsilateral muscle thickening combined with the lack of association with proptosis laterality or systemic biomarkers lend strong support to a model of contiguous inflammation over systemic autoimmunity,a hypothesis that warrants further validation through longitudinal and mechanistic studies.
基金the Start- up foundation of Fuzhou University ( 0 0 30 82 4 2 2 8),the Foundation ofDeveloping Science and Technical Developmentof Fuzhou University ( 2 0 0 3- QX- 2 1 ) and the Foundation ofScience and Technology of Fujian Province of PR China for Young
文摘A non-autonomous competing system is investigated in this paper,where the species x can diffuse between two patches of a heterogeneous environment with barriers between patches,but for species y,the diffusion does not involve a barrier between patches,further it is assumed that all the parameters are time dependent.It is shown that the system can be made persistent under some appropriate conditions.Moreover,sufficient conditions that guarantee the existence of a unique positive periodic orbit which is globally asymptotic stable are derived.
基金The project supported by the Innovation Foundation of Beihang University for Ph.D.Graduatesthe National Natural Science Foundation of China(60535010)
文摘This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.
文摘This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model.It focuses the attention on periodic orbits in the Earth-Moon system.This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies.Firstly,simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized,and periodic orbits around Lagrange points,either planar or three-dimensional,are intensively studied during past decades.Subsequently,stability index of a periodic orbit and bifurcation analysis are presented,which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals.Then,the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits,as well as constructing database of periodic orbits by numerical searching techniques are also presented.For those unstable periodic orbits,the station keeping maneuvers are reviewed.Finally,the applications of periodic orbits are presented,including those in practical missions,under consideration,and still in conceptual design stage.This review article has the function of bridging between engineers and researchers,so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem(RTBP).At the same time,it can also provide some technical thinking for general researchers.
基金Projects(NZ2013303,NZ2014201)supported by the National Natural Science Foundation of ChinaProjects(51375226,51305196,51475226)supported by the Fundamental Research Funds for the Central Universities,China
文摘A new non-linear bending-torsional coupled model for double-row planetary gear set was proposed, and planet's eccentricity error, static transmission error, and time-varying meshing stiffness were taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behaviors of dynamic load sharing characteristics affected by the system parameters including gear eccentricities error, ring gear's supporting stiffness, planet's bearing stiffness, torsional stiffness of first stage carrier and input rotation rate were investigated qualitatively and systematically, and sun gear radial orbits at first and second stage were explored as well. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA30010200)。
文摘Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.
基金supported by the National Natural Science Foundation of China (No.61174200)
文摘The dynamics of a rotating tethered satellite system （TSS） in the vicinity of libration points are highly nonlinear and inherently unstable. In order to fulfill the station-keep control of the rotating TSS along halo orbits, a nonlinear output tracking control scheme based on the θ- D technique is proposed. Compared with the popular time-variant linear quadratic regulator （LQR） controller, this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation. Besides, the obtained nonlinear suboptimal controller is in a closed form and easy to implement. Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors. The axis of rotation can keep pointing to an inertial specific object to fulfill an observation mission. In addition, the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.
基金was supported by the National Natural Science Foundation of China(No.61021002).
文摘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.
基金supported by National Natural Science Foundation of China(No.12172288)National Key Basic Research Program of China:Gravitational Wave Detection Project(Nos.2021YFC2202601 and 2021YFC2202603)General Program of Natural Science Foundation of Higher Education of Jiangsu Province(No.21KJB590001)。
文摘In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.
文摘The electron movement based on the multi-photon nonlinear Compton scattering with the extra-intense stationary laser field is discussed by using KMR (Kroll-Morton-Rosenbluth) theory.We find that there exists only an evolution from periodicity to non-periodicity of the un-captured electron phase orbits after the energy exchange between the electron beam and laser fields.With the increase of the absorbed photon number n by an electron, this evolution will be more and more faster, while it is rapidly decreased with the enhancement of the collision non-flexibility ξ of the electrons and photons; When the electrons are captured by the laser fields, the evolution is finished, the electrons will stably transport,and the photons dont give up the energy to these electrons.
基金the supports of the National Natural Science Foundation of China (Nos.11772009,11402007 and 11672007)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality
文摘An improved numerical method that can construct Halo/Lissajous orbits in the vicinity of collinear libration points in a full solar system model is investigated. A full solar system gravitational model in the geocentric rotating coordinate system with a clear presentation of the angular velocity relative to the inertial coordinate system is proposed. An alternative way to determine patch points in the multiple shooting method is provided based on a dynamical analysis with Poincare′sections. By employing the new patch points and sequential quadratic programming, Halo orbits for L1, L2, and L3points as well as Lissajous orbits for L1and L2points in the EarthMoon system are generated with the proposed full solar system gravitational model to verify the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Grants 11702333 and 11672337)Natural Science Foundation of Guangdong Province(Grant 2018B030311001).
文摘As a classical technique for chaos suppression,the time-delayed feedback controlling strategy has been widely developed by stabilizing unstable periodic orbits(UPOs)embedded in chaotic systems.A critical issue for achieving high controlling precision is to search for an appropriate time delay.This paper proposes a simple yet effective approach,based on incremental harmonic balance method,to determine the optimal time delay in the delayed feedback controller.The time delay is adjusted within the iterative scheme provided by the proposed method,and finally converges to the period of the target UPO.As long as the optimal time delay is fixed,moreover,the attained solution makes it quite convenient to analyze its stability according to the Floquet theory,which further provides the effective interval of the feedback gain.
基金Supported by National Natural Science Foundation of China (10771173)
文摘The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q（t） ＋ ↓△V（t, q（t）） = 0, where V（t, x） = -K（t, x） ＋ W（t, x）, K（t, x） is neither a quadratic form in x nor periodic in t and W（t, x） is superquadratic in x.
基金Project supported by the Science Foundation of Department of Education of Sichuan Province,China (Grant No.12233454)the Youth Foundation of Department of Education of Sichuan Province,China (Grant No.10ZB080)the Xihua University Foundation,China (Grant No.Z0913306)
文摘Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.
