This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present ...This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.展开更多
By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynami...By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynamics in close proximity to an asteroid,because it includes the perturbation caused by the gravitational orbit–attitude coupling of the spacecraft(GOACP).The GOACP is defined as the difference between the gravity acting on a non-spherical,extended body(the real case of a spacecraft)and the gravity acting on a point mass(the approximation of a spacecraft in classical orbital dynamics).Inplane equilibrium points that are within the principal planes of the asteroid have been investigated for the attitude-restricted orbital dynamics in previous studies,including equatorial and in-plane non-equatorial equilibrium points.In this study,out-of-plane equilibrium points outside the principal planes of the asteroid were examined.Out-ofplane equilibrium points cannot exist in the classical point-mass orbital dynamics but do exist in the attitude-restricted orbital dynamics owing to the effects of the GOACP.The previously investigated in-plane equilibrium points and the out-of-plane ones examined in this study provide a complete map of the equilibrium points in close proximity to an asteroid with the GOACP.Equatorial and in-plane non-equatorial equilibrium points have extended the longitude and latitude ranges of the classical equilibrium points without the GOACP,respectively,while the out-of-plane ones examined in the present study extend both the longitude and latitude ranges.Additionally,the invariant manifolds of out-of-plane equilibrium points were calculated,and the results indicated that the attitude of spacecraft significantly affects the invariant manifolds.In practice,these equilibrium points can provide natural hovering positions for operations in proximity to asteroids,and their invariant manifolds can be used for transfers to or from the equilibrium points.展开更多
A recently proposed orbital dynamics model in the close proximity of an asteroid,which is called“attitude-restricted orbital dynamics”,includes the perturbation caused by the spacecraft’s gravitational orbit-attitu...A recently proposed orbital dynamics model in the close proximity of an asteroid,which is called“attitude-restricted orbital dynamics”,includes the perturbation caused by the spacecraft’s gravitational orbit-attitude coupling.This orbital model improves the precision of classical point-mass orbital model with only the non-spherical gravity.Equatorial equilibrium points have been investigated in the previous paper.In this paper,the inplane non-equatorial equilibrium points,which are outside the asteroid’s equatorial plane but within its longitudinal principal plane,are further studied for a uniformly-rotating asteroid.These non-equatorial equilibrium points are more diverse than those in the classical point-mass orbital dynamics without gravitational orbit-attitude coupling perturbation(GOACP).Two families of them have been found.The equatorial equilibrium points studied before and the non-equatorial ones studied here give a complete map of equilibrium points in the asteroid’s principal planes.Compared with the classical point-mass orbital dynamics without GOACP,the equatorial equilibrium points have extended the longitude range of equilibrium points around an asteroid,while the non-equatorial ones studied here will extend the latitude range.These equatorial and non-equatorial equilibrium points provide natural hovering positions for the asteroid close-proximity operations.展开更多
The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of smal...The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.展开更多
This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium point...This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.展开更多
A molecular thermodynamic model was developed for describing the restricted swelling behavior of a thermosensitive hydrogel confined in a limited space. The Gibbs free energy includes two contributions, the contributi...A molecular thermodynamic model was developed for describing the restricted swelling behavior of a thermosensitive hydrogel confined in a limited space. The Gibbs free energy includes two contributions, the contribution of mixing of polymer and solvent calculated by using the lattice model of random polymer solution, and the contribution due to the elasticity of polymer network. This model can accurately describe the swelling behavior of restricted hydrogels under uniaxial and biaxial constraints by using two model parameters. One is the interaction energy parameter between polymer network and solvent, and the other is the size parameter depending on the degree of cross-linking. The calculated results show that the swelling ratio reduces significantly and the phase transition temperature decreases slightly as the restricted degree increases, which agree well with the experimental data.展开更多
We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has ...We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.展开更多
基金Research Partnership Program no.RP-21-09-06 from the Deanship of Scientific Research of Imam Mohammad Ibn Saud Islamic University(IMSIU).
文摘This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.
基金supported by the National Natural Science Foundation of China under Grant Nos.11602009,11432001 and 11872007the Fundamental Research Funds for the Central Universities.
文摘By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynamics in close proximity to an asteroid,because it includes the perturbation caused by the gravitational orbit–attitude coupling of the spacecraft(GOACP).The GOACP is defined as the difference between the gravity acting on a non-spherical,extended body(the real case of a spacecraft)and the gravity acting on a point mass(the approximation of a spacecraft in classical orbital dynamics).Inplane equilibrium points that are within the principal planes of the asteroid have been investigated for the attitude-restricted orbital dynamics in previous studies,including equatorial and in-plane non-equatorial equilibrium points.In this study,out-of-plane equilibrium points outside the principal planes of the asteroid were examined.Out-ofplane equilibrium points cannot exist in the classical point-mass orbital dynamics but do exist in the attitude-restricted orbital dynamics owing to the effects of the GOACP.The previously investigated in-plane equilibrium points and the out-of-plane ones examined in this study provide a complete map of the equilibrium points in close proximity to an asteroid with the GOACP.Equatorial and in-plane non-equatorial equilibrium points have extended the longitude and latitude ranges of the classical equilibrium points without the GOACP,respectively,while the out-of-plane ones examined in the present study extend both the longitude and latitude ranges.Additionally,the invariant manifolds of out-of-plane equilibrium points were calculated,and the results indicated that the attitude of spacecraft significantly affects the invariant manifolds.In practice,these equilibrium points can provide natural hovering positions for operations in proximity to asteroids,and their invariant manifolds can be used for transfers to or from the equilibrium points.
基金This work has been supported by the National Natural Science Foundation of China under Grant Nos.11602009,11432001,and 11872007the Young Elite Scientist Sponsorship Program by China Association for Science and Technology under Grant No.2017QNRC001the Fundamental Research Funds for the Central Universities.
文摘A recently proposed orbital dynamics model in the close proximity of an asteroid,which is called“attitude-restricted orbital dynamics”,includes the perturbation caused by the spacecraft’s gravitational orbit-attitude coupling.This orbital model improves the precision of classical point-mass orbital model with only the non-spherical gravity.Equatorial equilibrium points have been investigated in the previous paper.In this paper,the inplane non-equatorial equilibrium points,which are outside the asteroid’s equatorial plane but within its longitudinal principal plane,are further studied for a uniformly-rotating asteroid.These non-equatorial equilibrium points are more diverse than those in the classical point-mass orbital dynamics without gravitational orbit-attitude coupling perturbation(GOACP).Two families of them have been found.The equatorial equilibrium points studied before and the non-equatorial ones studied here give a complete map of equilibrium points in the asteroid’s principal planes.Compared with the classical point-mass orbital dynamics without GOACP,the equatorial equilibrium points have extended the longitude range of equilibrium points around an asteroid,while the non-equatorial ones studied here will extend the latitude range.These equatorial and non-equatorial equilibrium points provide natural hovering positions for the asteroid close-proximity operations.
文摘The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters;the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points;whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.
文摘This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.
基金Supported by the National Natural Science Foundation of China(21076071,21276074)the 111 Project of the Ministry of Education of China(B08021)the Fundamental Research Funds for the Central Universities of China
文摘A molecular thermodynamic model was developed for describing the restricted swelling behavior of a thermosensitive hydrogel confined in a limited space. The Gibbs free energy includes two contributions, the contribution of mixing of polymer and solvent calculated by using the lattice model of random polymer solution, and the contribution due to the elasticity of polymer network. This model can accurately describe the swelling behavior of restricted hydrogels under uniaxial and biaxial constraints by using two model parameters. One is the interaction energy parameter between polymer network and solvent, and the other is the size parameter depending on the degree of cross-linking. The calculated results show that the swelling ratio reduces significantly and the phase transition temperature decreases slightly as the restricted degree increases, which agree well with the experimental data.
基金Supported by the National Natural Science Foundation of China
文摘We found another critical mass ratio value -↑μ between μ4 and μ5 concerning the genealogy of the long period family around the equilateral equilibrium point L4 in the restricted three-body problem. This value has not been pointed out before. We used numerical computations to show how the long period family evolves around this critical value. The case is similar to that of the critical values between μ2 and μ4, with slight difference in evolution details.
