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 phys...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
We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product(MVP)for N-body problems in d dimensions,namely efficient H^(2)_(∗)(fully nested algorithm,i.e.,H^(2)matrix a...We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product(MVP)for N-body problems in d dimensions,namely efficient H^(2)_(∗)(fully nested algorithm,i.e.,H^(2)matrix algorithm)and(H^(2)+H)_(∗)(semi-nested algorithm,i.e.,cross of H^(2)and H matrix algorithms).The efficient H^(2)_(∗)and(H^(2)+H)_(∗)hierarchical representations are based on our recently introduced weak admissibility condition in higher dimensions(Khan et al.,J.Comput.Phys.2024),where the admissible clusters are the far-field and the vertex-sharing clusters.Due to the use of nested form of the bases,the proposed hierarchical matrix algorithms are more efficient than the non-nested algorithms(H matrix algorithms).We rely on purely algebraic low-rank approximation techniques(e.g.,ACA(Bebendorf et al.,Computing 2003)and NCA(Bebendorf et al.,Numer.Math.2012;Gujjula and Ambikasaran,arXiv:2203.148322022;Zhao et al.,IEEE Trans.Microw.Theory Tech.2019))and develop both algorithms in a black-box(kernel-independent)fashion.The initialization time of the proposed algorithms scales quasi-linearly,i.e.,complexity O(Nlog^(α)(N)),α≥0 and small.Using the proposed hierarchical representations,one can perform theMVP that scales at most quasi-linearly.Another noteworthy contribution of this article is that we perform a comparative study of the proposed algorithms with different algebraic(NCA or ACA-based compression)fast MVP algorithms(e.g.,H^(2),H,etc.)in 2D and 3D(d=2,3).The fast algorithms are tested on various kernel matrices and applied to get fast iterative solutions of a dense linear system arising from the discretized integral equations and radial basis function interpolation.The article also discusses the scalability of the algorithms and provides various benchmarks.Notably,all the algorithms are developed in a similar fashion in C++and tested within the same environment,allowing for meaningful comparisons.The numerical results demonstrate that the proposed algorithms are competitive to the NCA-based standard H^(2)matrix algorithm(where the admissible clusters are the far-field clusters)with respect to the memory and time.The C++implementation of the proposed algorithms is available at https://github.com/riteshkhan/H^(2)weak/.展开更多
A large database is desired for machine learning(ML) technology to make accurate predictions of materials physicochemical properties based on their molecular structure.When a large database is not available,the develo...A large database is desired for machine learning(ML) technology to make accurate predictions of materials physicochemical properties based on their molecular structure.When a large database is not available,the development of proper featurization method based on physicochemical nature of target proprieties can improve the predictive power of ML models with a smaller database.In this work,we show that two new featurization methods,volume occupation spatial matrix and heat contribution spatial matrix,can improve the accuracy in predicting energetic materials' crystal density(ρ_(crystal)) and solid phase enthalpy of formation(H_(f,solid)) using a database containing 451 energetic molecules.Their mean absolute errors are reduced from 0.048 g/cm~3 and 24.67 kcal/mol to 0.035 g/cm~3 and 9.66 kcal/mol,respectively.By leave-one-out-cross-validation,the newly developed ML models can be used to determine the performance of most kinds of energetic materials except cubanes.Our ML models are applied to predict ρ_(crystal) and H_(f,solid) of CHON-based molecules of the 150 million sized PubChem database,and screened out 56 candidates with competitive detonation performance and reasonable chemical structures.With further improvement in future,spatial matrices have the potential of becoming multifunctional ML simulation tools that could provide even better predictions in wider fields of materials science.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We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product(MVP)for N-body problems in d dimensions,namely efficient H^(2)_(∗)(fully nested algorithm,i.e.,H^(2)matrix algorithm)and(H^(2)+H)_(∗)(semi-nested algorithm,i.e.,cross of H^(2)and H matrix algorithms).The efficient H^(2)_(∗)and(H^(2)+H)_(∗)hierarchical representations are based on our recently introduced weak admissibility condition in higher dimensions(Khan et al.,J.Comput.Phys.2024),where the admissible clusters are the far-field and the vertex-sharing clusters.Due to the use of nested form of the bases,the proposed hierarchical matrix algorithms are more efficient than the non-nested algorithms(H matrix algorithms).We rely on purely algebraic low-rank approximation techniques(e.g.,ACA(Bebendorf et al.,Computing 2003)and NCA(Bebendorf et al.,Numer.Math.2012;Gujjula and Ambikasaran,arXiv:2203.148322022;Zhao et al.,IEEE Trans.Microw.Theory Tech.2019))and develop both algorithms in a black-box(kernel-independent)fashion.The initialization time of the proposed algorithms scales quasi-linearly,i.e.,complexity O(Nlog^(α)(N)),α≥0 and small.Using the proposed hierarchical representations,one can perform theMVP that scales at most quasi-linearly.Another noteworthy contribution of this article is that we perform a comparative study of the proposed algorithms with different algebraic(NCA or ACA-based compression)fast MVP algorithms(e.g.,H^(2),H,etc.)in 2D and 3D(d=2,3).The fast algorithms are tested on various kernel matrices and applied to get fast iterative solutions of a dense linear system arising from the discretized integral equations and radial basis function interpolation.The article also discusses the scalability of the algorithms and provides various benchmarks.Notably,all the algorithms are developed in a similar fashion in C++and tested within the same environment,allowing for meaningful comparisons.The numerical results demonstrate that the proposed algorithms are competitive to the NCA-based standard H^(2)matrix algorithm(where the admissible clusters are the far-field clusters)with respect to the memory and time.The C++implementation of the proposed algorithms is available at https://github.com/riteshkhan/H^(2)weak/.
基金support from the Ministry of Education(MOE) Singapore Tier 1 (RG8/20)。
文摘A large database is desired for machine learning(ML) technology to make accurate predictions of materials physicochemical properties based on their molecular structure.When a large database is not available,the development of proper featurization method based on physicochemical nature of target proprieties can improve the predictive power of ML models with a smaller database.In this work,we show that two new featurization methods,volume occupation spatial matrix and heat contribution spatial matrix,can improve the accuracy in predicting energetic materials' crystal density(ρ_(crystal)) and solid phase enthalpy of formation(H_(f,solid)) using a database containing 451 energetic molecules.Their mean absolute errors are reduced from 0.048 g/cm~3 and 24.67 kcal/mol to 0.035 g/cm~3 and 9.66 kcal/mol,respectively.By leave-one-out-cross-validation,the newly developed ML models can be used to determine the performance of most kinds of energetic materials except cubanes.Our ML models are applied to predict ρ_(crystal) and H_(f,solid) of CHON-based molecules of the 150 million sized PubChem database,and screened out 56 candidates with competitive detonation performance and reasonable chemical structures.With further improvement in future,spatial matrices have the potential of becoming multifunctional ML simulation tools that could provide even better predictions in wider fields of materials science.
