An increasing number of drivers are relying on digital map navigation systems in vehicles or mobile phones to select optimal driving routes in order to save time and improve safety. In the near future, digital map nav...An increasing number of drivers are relying on digital map navigation systems in vehicles or mobile phones to select optimal driving routes in order to save time and improve safety. In the near future, digital map navigation systems are expected to play more important roles in transportation systems. In order to extend current navigation systems to more applications, two fundamental problems must be resolved: the lane-level map model and lane-level route planning. This study proposes solutions to both problems. The current limitation of the lane-level map model is not its accuracy but its flexibility;this study proposes a novel seven-layer map structure, called as Tsinghua map model, which is able to support autonomous driving in a flexible and efficient way. For lane-level route planning, we propose a hierarchical route-searching algorithm to accelerate the planning process, even in the presence of complicated lane networks. In addition, we model the travel costs allocated for lane-level road networks by analyzing vehicle maneuvers in traversing lanes, changing lanes, and turning at intersections. Tests were performed on both a grid network and a real lane-level road network to demonstrate the validity and efficiency of the proposed algorithm.展开更多
In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature,...In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature, the source term addresses the impact of speed difference and density difference between adjacent lanes, which provides better precision for free lane-changing simulation; the viscosity term turns lane-changing behavior to a ＂force＂ that may influence speed distribution. Using a flux-splitting scheme for the model discretization, two cases are investigated numerically. The case under a homogeneous initial condition shows that the numerical results by our model agree well with the analytical ones; the case with a small initial disturbance shows that our model can simulate the evolution of perturbation, including propagation,dissipation, cluster effect and stop-and-go phenomenon.展开更多
In the field of traffic flow studies, compulsive lane-changing refers to lane-changing （LC） behaviors due to traffic rules or bad road conditions, while free LC happens when drivers change lanes to drive on a faster...In the field of traffic flow studies, compulsive lane-changing refers to lane-changing （LC） behaviors due to traffic rules or bad road conditions, while free LC happens when drivers change lanes to drive on a faster or less crowded lane. LC studies based on differential equation models accurately reveal LC influence on traffic environment. This paper presents a second-order partial differential equation （PDE） model that simulates both compulsive LC behavior and free LC behavior, with lane-changing source terms in the continuity equation and a lane-changing viscosity term in the momentum equation. A specific form of this model focusing on a typical compulsive LC behavior, the ＇off-ramp problem＇, is derived. Numerical simulations are given in several cases, which are consistent with real traffic phenomenon.展开更多
Lane-Emden type equation is a nonlinear differential equation appears in many fields such as stellar structure, radioactive cooling and modeling of clusters of galaxies. In this work, this equation is investigated usi...Lane-Emden type equation is a nonlinear differential equation appears in many fields such as stellar structure, radioactive cooling and modeling of clusters of galaxies. In this work, this equation is investigated using a semi-analytical method called the Variation of parameters method with an auxiliary parameter. In the applied technique, an unknown auxiliary parameter is inserted in Variation of Parameters Method to solve some special cases of these equations. The used algorithm is easy to implement and very effective. The obtained solutions are also fairly accurate.展开更多
We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is b...We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is bounded and that the solutions are monotone decreasing. The upper bound, the value of the solution at zero, can be approximated analytically in terms of the physical parameters. We obtain solutions to the boundary value problem, using both the Taylor series （which work well for weak nonlinearity） and the b-expansion method （valid for strong nonlinearity）. From here, we are able to deduce the qualitative behavior of the solution profiles with a change in any one of the physical parameters.展开更多
In the present paper, two new generating sets, of homology invariant functions will be established. Moreover, by the aid of two independent homology invariant functions of each set we established the transformed first...In the present paper, two new generating sets, of homology invariant functions will be established. Moreover, by the aid of two independent homology invariant functions of each set we established the transformed first order Lane-Emden equation. The first equation for polytropic index n ≠–1, ±∞ depends on five free parameters, while the other equation is for, n = ±∞ and depends on three free parameters.展开更多
Lane-Emden differential equations of order fractional has been studied.Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analyt...Lane-Emden differential equations of order fractional has been studied.Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.展开更多
In this work we apply the differential transformation method or DTM for solving some classes of Lane-Emden type equations as a model for the dimensionless density distribution in an isothermal gas sphere and as a stud...In this work we apply the differential transformation method or DTM for solving some classes of Lane-Emden type equations as a model for the dimensionless density distribution in an isothermal gas sphere and as a study of the gravitational potential of (white-dwarf) stars , which are nonlinear ordinary differential equations on the semi-infinite domain [1] [2]. The efficiency of the DTM is illustrated by investigating the convergence results for this type of the Lane-Emden equations. The numerical results show the reliability and accuracy of this method.展开更多
Ship.to.ship, ship.to.shore radio links empowered by Wi Fi, Wi MAX etc have been recently exploited to build maritime multi.hop mesh networks to provide internet services to on.ship users. However, because of the mobi...Ship.to.ship, ship.to.shore radio links empowered by Wi Fi, Wi MAX etc have been recently exploited to build maritime multi.hop mesh networks to provide internet services to on.ship users. However, because of the mobility of the vessels/ships and the large inter.ship distances, nodes in the maritime network are frequently disconnected, forcing data communication in the maritime mesh networks to be opportunistic and delay.tolerant. In this paper, we present Lane Post, an optimization approach for maritime delay.tolerant routing protocol. We exploit the shipping lane information to predict the rendezvous opportunities of the ships to optimize the route selection in delay.tolerant routing. In particular, we show that when the shipping lane information is available, an opportunistic routing graph(ORG) for each ship can be constructed to predict its multi.hop data routing opportunities to the other ships or to the shore. Based on the ORG, we develop an optimal route protocol(i.e., Lane Post) for each ship to minimize its delay of multi.hop packet delivery via dynamic programming. We discussed the ways of collecting shipping lane information by centralized method or distributed method.The proposed Lane Post protocol was evaluated by ONE, an open.source delay.tolerant network simulator, which shows its dramatic performance improvement in terms of delay reduction compared to the state.of.the.art opportunistic routing protocols.展开更多
基金the National Key Research and Development Program of China (2018YFB0105000)the National Natural Science Foundation of China (61773234 and U1864203)+2 种基金the Project of Tsinghua University and Toyota Joint Research Center for AI Technology of Automated Vehicle (TT2018-02)the International Science and Technology Cooperation Program of China (2016YFE0102200)the software developed in the Beijing Municipal Science and Technology Program (D171100005117001 and Z181100005918001).
文摘An increasing number of drivers are relying on digital map navigation systems in vehicles or mobile phones to select optimal driving routes in order to save time and improve safety. In the near future, digital map navigation systems are expected to play more important roles in transportation systems. In order to extend current navigation systems to more applications, two fundamental problems must be resolved: the lane-level map model and lane-level route planning. This study proposes solutions to both problems. The current limitation of the lane-level map model is not its accuracy but its flexibility;this study proposes a novel seven-layer map structure, called as Tsinghua map model, which is able to support autonomous driving in a flexible and efficient way. For lane-level route planning, we propose a hierarchical route-searching algorithm to accelerate the planning process, even in the presence of complicated lane networks. In addition, we model the travel costs allocated for lane-level road networks by analyzing vehicle maneuvers in traversing lanes, changing lanes, and turning at intersections. Tests were performed on both a grid network and a real lane-level road network to demonstrate the validity and efficiency of the proposed algorithm.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11002035 and 11372147)Hui-Chun Chin and Tsung-Dao Lee Chinese Undergraduate Research Endowment(Grant No.CURE 14024)
文摘In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature, the source term addresses the impact of speed difference and density difference between adjacent lanes, which provides better precision for free lane-changing simulation; the viscosity term turns lane-changing behavior to a ＂force＂ that may influence speed distribution. Using a flux-splitting scheme for the model discretization, two cases are investigated numerically. The case under a homogeneous initial condition shows that the numerical results by our model agree well with the analytical ones; the case with a small initial disturbance shows that our model can simulate the evolution of perturbation, including propagation,dissipation, cluster effect and stop-and-go phenomenon.
基金supported by the National Natural Science Foundation of China(Grant Nos.11002035 and 11372147)
文摘In the field of traffic flow studies, compulsive lane-changing refers to lane-changing （LC） behaviors due to traffic rules or bad road conditions, while free LC happens when drivers change lanes to drive on a faster or less crowded lane. LC studies based on differential equation models accurately reveal LC influence on traffic environment. This paper presents a second-order partial differential equation （PDE） model that simulates both compulsive LC behavior and free LC behavior, with lane-changing source terms in the continuity equation and a lane-changing viscosity term in the momentum equation. A specific form of this model focusing on a typical compulsive LC behavior, the ＇off-ramp problem＇, is derived. Numerical simulations are given in several cases, which are consistent with real traffic phenomenon.
文摘Lane-Emden type equation is a nonlinear differential equation appears in many fields such as stellar structure, radioactive cooling and modeling of clusters of galaxies. In this work, this equation is investigated using a semi-analytical method called the Variation of parameters method with an auxiliary parameter. In the applied technique, an unknown auxiliary parameter is inserted in Variation of Parameters Method to solve some special cases of these equations. The used algorithm is easy to implement and very effective. The obtained solutions are also fairly accurate.
基金supported by the National Science Foundation of U.S.A.(No.1144246)
文摘We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is bounded and that the solutions are monotone decreasing. The upper bound, the value of the solution at zero, can be approximated analytically in terms of the physical parameters. We obtain solutions to the boundary value problem, using both the Taylor series （which work well for weak nonlinearity） and the b-expansion method （valid for strong nonlinearity）. From here, we are able to deduce the qualitative behavior of the solution profiles with a change in any one of the physical parameters.
文摘In the present paper, two new generating sets, of homology invariant functions will be established. Moreover, by the aid of two independent homology invariant functions of each set we established the transformed first order Lane-Emden equation. The first equation for polytropic index n ≠–1, ±∞ depends on five free parameters, while the other equation is for, n = ±∞ and depends on three free parameters.
文摘Lane-Emden differential equations of order fractional has been studied.Numerical solution of this type is considered by collocation method. Some of examples are illustrated. The comparison between numerical and analytic methods has been introduced.
文摘In this work we apply the differential transformation method or DTM for solving some classes of Lane-Emden type equations as a model for the dimensionless density distribution in an isothermal gas sphere and as a study of the gravitational potential of (white-dwarf) stars , which are nonlinear ordinary differential equations on the semi-infinite domain [1] [2]. The efficiency of the DTM is illustrated by investigating the convergence results for this type of the Lane-Emden equations. The numerical results show the reliability and accuracy of this method.
基金supported in part by National Natural Science Foundation of China Grant 61672524the Fundamental Research Funds for the Central University+1 种基金the Research Funds of Renmin University of China, 2015030273National Key Technology Support Program 2014BAK12B06
文摘Ship.to.ship, ship.to.shore radio links empowered by Wi Fi, Wi MAX etc have been recently exploited to build maritime multi.hop mesh networks to provide internet services to on.ship users. However, because of the mobility of the vessels/ships and the large inter.ship distances, nodes in the maritime network are frequently disconnected, forcing data communication in the maritime mesh networks to be opportunistic and delay.tolerant. In this paper, we present Lane Post, an optimization approach for maritime delay.tolerant routing protocol. We exploit the shipping lane information to predict the rendezvous opportunities of the ships to optimize the route selection in delay.tolerant routing. In particular, we show that when the shipping lane information is available, an opportunistic routing graph(ORG) for each ship can be constructed to predict its multi.hop data routing opportunities to the other ships or to the shore. Based on the ORG, we develop an optimal route protocol(i.e., Lane Post) for each ship to minimize its delay of multi.hop packet delivery via dynamic programming. We discussed the ways of collecting shipping lane information by centralized method or distributed method.The proposed Lane Post protocol was evaluated by ONE, an open.source delay.tolerant network simulator, which shows its dramatic performance improvement in terms of delay reduction compared to the state.of.the.art opportunistic routing protocols.
