Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can b...Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can be applied to other metals. The dislocation emission from a crack tip has been simulated successfully using molecular dynamics method, the result is in good agreement with the elastic solution.展开更多
The N-body problem in classical physics, is the calculation of force ofgravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to phy...The N-body problem in classical physics, is the calculation of force ofgravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to physicists andmathematicians. Large number of bodies, huge masses, long distances and exponentially increasing number of equations of motion of the bodies have been themajor hurdles in solving this problem for large and complex galaxies. Adventof high performance computational machines have mitigated the problem to muchextent, but still for large number of bodies it consumes huge amount of resourcesand days for computation. Conventional algorithms have been able to reduce thecomputational complexity from O n2 ð Þ to O nlogn ð Þ by splitting the space into atree or mesh network, researchers are still looking for improvements. In thisresearch work we propose a novel solution to N-body problem inspired by metaheuristics algorithms. The proposed algorithm is simulated for various time periods of selected heavenly bodies and analyzed for speed and accuracy. Theresults are compared with that of conventional algorithms. The outcomes showabout 50% time saving with almost no loss in accuracy. The proposed approachbeing a metaheuristics optimization technique, attempts to find optimal solution tothe problem, searching the entire space in a unique and efficient manner in a verylimited amount of time.展开更多
A two-body regularization for N-body problem based on perturbation theory for Keplerian problem is discussed. We provide analytical estimations of accuracy and conduct N-body experiments in order to compare it with st...A two-body regularization for N-body problem based on perturbation theory for Keplerian problem is discussed. We provide analytical estimations of accuracy and conduct N-body experiments in order to compare it with state-of-the-art Hermite integrator. It is shown that this regularization keeps some features that allow overcoming KS-regularization in some particular cases.展开更多
The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physica...The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physical parameters and a similarity method which permits a manifold reduction of the calculation time for the evolution of “large” systems. This is done by averaging the results of calculations over an ensemble of many “small” systems with total particle number in the ensemble equal to the number of stars in the large system. The method is valid for the approximate calculation of the evolution of large systems, including dissipative systems like AGN containing a supermassive black hole, accretion disc, and the surrounding stellar cluster.展开更多
Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal...Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal behavior of different physical parameters of active galactic nuclei (AGN) containing a super massive black hole (SMBH), an accretion disk, and a compact stellar cluster;2) calculation of the stellar capture rate to the central SMBH without accretion disk. The calculations show good perspectives for applications of the similarity method to optimize the evolution model calculations of large stellar systems and of AGN.展开更多
In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to ea...In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.展开更多
For n-body problems with quasihomogeneous potentials in ?k (2[ n/2] ? k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin...For n-body problems with quasihomogeneous potentials in ?k (2[ n/2] ? k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n - 1 simplex with fixed side length.展开更多
The authors consider non-autonomous N-body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity.Using Ljusternik-Schnirelmann theory,the authors prove the existence of unb...The authors consider non-autonomous N-body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity.Using Ljusternik-Schnirelmann theory,the authors prove the existence of unbounded sequences of critical values for the Lagrangian action corresponding to non-collision periodic solutions.展开更多
In this study,an N-body simulation code was developed for self-gravitating systems with a limited first-order post-Newtonian approximation.The code was applied to a special case in which the system consists of one mas...In this study,an N-body simulation code was developed for self-gravitating systems with a limited first-order post-Newtonian approximation.The code was applied to a special case in which the system consists of one massive object and many low-mass objects.Therefore,the behavior of stars around the massive black hole could be analyzed.A graphics processing unit(GPU)was used to accelerate the code exe-cution,and it could be accelerated by several tens of times compared to a single-core CPU for N≃104 objects.展开更多
Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanic...Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanics. It is necessary to set the coordinates, velocities and masses of the stars so that as a result of their gravitational interaction the globular cluster is not destroyed. This is not an easy task, and it has been solved in this paper. Using an exact solution of the axisymmetric gravitational interaction of N-bodies, single-layer spherical structures were created. They are combined into multilayer models of globular clusters. An algorithm and a program for their creation is described. As a result of solving the problem of gravitational interaction of N bodies, evolution of 5-, 10-, and 15-layer structures was studied. During the inter-body interaction, there proceeds a transition from the initial specially organized structure to a structure with bodies, uniformly distributed in space. The number of inter-body collisions decreases, and the globular cluster model passes into the stable form of its existence. The collisions of bodies and the acquisition of rotational motion and thermal energy by them are considered. As a result of the passage to scaled dimensions, the results were recalculated to the conditions of globular star clusters. The periods of rotation and the temperatures of merged stars are calculated. Attention is paid to a decreased central-body mass in the analyzed models of globular star clusters.展开更多
We have investigated the role that different galaxy types have in galaxy-galaxy interactions in compact groups. N-body simulations of 6 galaxies consisting of a differing mixture of galaxy types were run to compare th...We have investigated the role that different galaxy types have in galaxy-galaxy interactions in compact groups. N-body simulations of 6 galaxies consisting of a differing mixture of galaxy types were run to compare the relative importance of galaxy population demographic on evolution. Three different groups with differing galaxy content were tested: all spiral, a single elliptical and 50% elliptical. Tidal interaction strength and duration were recorded to assess the importance of an interaction. A group with an equal number of spiral and elliptical galaxies has some of the longest and strongest interactions with elliptical-elliptical interactions being most significant. These elliptical-elliptical interactions are not dominated by a single large event but consist of multiple interactions. Elliptical galaxies tidally interacting with spiral galaxies, have the next strongest interaction events. For the case when a group only has a single elliptical, the largest magnitude tidal interaction is an elliptical on a spiral. Spirals interact with each other through many small interactions. For a spiral only group, the interactions are the weakest compared to the other group types. These spiral interactions are not dominated by any singular event that might be expected to lead to a merger but are more of an ongoing harassment. These results suggest that within a compact group, early type galaxies will not form via merger out of an assemblage of spiral galaxies but rather that compact groups, in effect form around an early type galaxy.展开更多
基金The project supported by the National Natural Science Foundation of China
文摘Based on the embedded atom method (EAM) proposed by Daw and Baskes and Johnson's model, this paper constructs a new N-body potential for bcc crystal Mo. The procedure of constructing the new N-body potential can be applied to other metals. The dislocation emission from a crack tip has been simulated successfully using molecular dynamics method, the result is in good agreement with the elastic solution.
基金This research study has been supported by National Center in Big Data and Cloud Computing,NED University of Engincering and Technology,Karachi,Pakistan.
文摘The N-body problem in classical physics, is the calculation of force ofgravitational attraction of heavenly bodies towards each other. Solving this problem for many heavenly bodies has always posed a challenge to physicists andmathematicians. Large number of bodies, huge masses, long distances and exponentially increasing number of equations of motion of the bodies have been themajor hurdles in solving this problem for large and complex galaxies. Adventof high performance computational machines have mitigated the problem to muchextent, but still for large number of bodies it consumes huge amount of resourcesand days for computation. Conventional algorithms have been able to reduce thecomputational complexity from O n2 ð Þ to O nlogn ð Þ by splitting the space into atree or mesh network, researchers are still looking for improvements. In thisresearch work we propose a novel solution to N-body problem inspired by metaheuristics algorithms. The proposed algorithm is simulated for various time periods of selected heavenly bodies and analyzed for speed and accuracy. Theresults are compared with that of conventional algorithms. The outcomes showabout 50% time saving with almost no loss in accuracy. The proposed approachbeing a metaheuristics optimization technique, attempts to find optimal solution tothe problem, searching the entire space in a unique and efficient manner in a verylimited amount of time.
文摘A two-body regularization for N-body problem based on perturbation theory for Keplerian problem is discussed. We provide analytical estimations of accuracy and conduct N-body experiments in order to compare it with state-of-the-art Hermite integrator. It is shown that this regularization keeps some features that allow overcoming KS-regularization in some particular cases.
文摘The theoretical foundation of a new N-body simulation method for the dynamics of large numbers (N > 106) of gravitating bodies is described. The new approach is founded on the probability description of the physical parameters and a similarity method which permits a manifold reduction of the calculation time for the evolution of “large” systems. This is done by averaging the results of calculations over an ensemble of many “small” systems with total particle number in the ensemble equal to the number of stars in the large system. The method is valid for the approximate calculation of the evolution of large systems, including dissipative systems like AGN containing a supermassive black hole, accretion disc, and the surrounding stellar cluster.
文摘Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal behavior of different physical parameters of active galactic nuclei (AGN) containing a super massive black hole (SMBH), an accretion disk, and a compact stellar cluster;2) calculation of the stellar capture rate to the central SMBH without accretion disk. The calculations show good perspectives for applications of the similarity method to optimize the evolution model calculations of large stellar systems and of AGN.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871096), QSSTE and MOST.
文摘In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.
基金This work was supported by MSTC, the National Natural Science Foundation of China and QSSTF.
文摘For n-body problems with quasihomogeneous potentials in ?k (2[ n/2] ? k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n - 1 simplex with fixed side length.
基金supported by the National Natural Science Foundation of China(Nos.11701463,11671278).
文摘The authors consider non-autonomous N-body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity.Using Ljusternik-Schnirelmann theory,the authors prove the existence of unbounded sequences of critical values for the Lagrangian action corresponding to non-collision periodic solutions.
文摘In this study,an N-body simulation code was developed for self-gravitating systems with a limited first-order post-Newtonian approximation.The code was applied to a special case in which the system consists of one massive object and many low-mass objects.Therefore,the behavior of stars around the massive black hole could be analyzed.A graphics processing unit(GPU)was used to accelerate the code exe-cution,and it could be accelerated by several tens of times compared to a single-core CPU for N≃104 objects.
文摘Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanics. It is necessary to set the coordinates, velocities and masses of the stars so that as a result of their gravitational interaction the globular cluster is not destroyed. This is not an easy task, and it has been solved in this paper. Using an exact solution of the axisymmetric gravitational interaction of N-bodies, single-layer spherical structures were created. They are combined into multilayer models of globular clusters. An algorithm and a program for their creation is described. As a result of solving the problem of gravitational interaction of N bodies, evolution of 5-, 10-, and 15-layer structures was studied. During the inter-body interaction, there proceeds a transition from the initial specially organized structure to a structure with bodies, uniformly distributed in space. The number of inter-body collisions decreases, and the globular cluster model passes into the stable form of its existence. The collisions of bodies and the acquisition of rotational motion and thermal energy by them are considered. As a result of the passage to scaled dimensions, the results were recalculated to the conditions of globular star clusters. The periods of rotation and the temperatures of merged stars are calculated. Attention is paid to a decreased central-body mass in the analyzed models of globular star clusters.
文摘We have investigated the role that different galaxy types have in galaxy-galaxy interactions in compact groups. N-body simulations of 6 galaxies consisting of a differing mixture of galaxy types were run to compare the relative importance of galaxy population demographic on evolution. Three different groups with differing galaxy content were tested: all spiral, a single elliptical and 50% elliptical. Tidal interaction strength and duration were recorded to assess the importance of an interaction. A group with an equal number of spiral and elliptical galaxies has some of the longest and strongest interactions with elliptical-elliptical interactions being most significant. These elliptical-elliptical interactions are not dominated by a single large event but consist of multiple interactions. Elliptical galaxies tidally interacting with spiral galaxies, have the next strongest interaction events. For the case when a group only has a single elliptical, the largest magnitude tidal interaction is an elliptical on a spiral. Spirals interact with each other through many small interactions. For a spiral only group, the interactions are the weakest compared to the other group types. These spiral interactions are not dominated by any singular event that might be expected to lead to a merger but are more of an ongoing harassment. These results suggest that within a compact group, early type galaxies will not form via merger out of an assemblage of spiral galaxies but rather that compact groups, in effect form around an early type galaxy.
