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References

Aar63
Aarseth Sverre J. (1963) Dynamical evolution of clusters of galaxies, i. 126: 223--255.

Aar85
Aarseth S. J. (1985) Direct methods for n-body simulations. In Blackbill J. U. and Cohen B. I. (eds) Multiple Time Scales, pages 377--418. Academic Press, New York.

ADG+85
Applegate J. H., Douglas M. R., Gursel Y., Huner P., Seitz C. L., and Sussman G. J. (1985) A digital orrery. IEEE Transactions on Computers C-34: 822--831.

And92
Anderson C. R. (1992) An implementation of the fast multipole method without multipoles. SIAM Journal on Scientific and Statistical Computing 13: 923--947.

App85
Appel A. W. (January 1985) An efficient program for many-body simulation. SIAM Journal on Scientific and Statistical Computing 6: 85--103.

AW86
Aguilar L. A. and White S. D. M. (1986) The density profiles of tidally stripped galaxies. 307: 97--109.

BH86
Barnes J. and Hut P. (1986) A hiearchical o(nlogn) force calculation algorithm. Nature 324: 446--449.

BHER95
Board J. A. J., Hakura Z. S., Elliott W. D., and Rankin W. T. (1995) Scalable variants of multipole-based algorithms for molecular dynamics applications. In et al. D. H. B. (ed) Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, pages 295--300. SIAM, Philadelphia.

BS97
Blackston D. and Suel T. (1997) Highly portable and efficient implementations of parallel adaptive n-body methods. In Proceedings of SC97, pages (CD--ROM). ACM.

Cha43
Chandrasekhar S. (1943) Principles of Stellar Dynamics. Dover, New York.

CSS93
Calvo M. P. and Sanz-Serna J. M. (1993) The development of variable-step symplectic integrators, with application to the two-body problem. SIAM J. Sci. Comput. 14: 936--952.

CSS97
Cano B. and Sanz-Serna J. M. (1997) Error growth in the numerical integration of periodic orbots, with application to hamiltonian and reversible systems. SIAM J. Num. Anal. 34.

CTP95
Couchman H. M. P., Thomas P. A., and Pearce F. R. (October 1995) Hydra: an adaptive-mesh implementation of p 3m-sph. 452: 797+.

EIN93
Emori H., Ida S., and Nakazawa K. (1993) New method for the numerical integration of an n-body system in an external potential. 45: 321--327.

EJ96
Elliott W. D. and Jr. J. A. B. (March 1996) Fast fourier transform accelerated fast multipole algorithm. SIAM Journal on Scientific Computing 17: 398--415.

ET99
Evans N. W. and Tremaine S. (October 1999) Linear multistep methods for integrating reversible differential equations. 118: 1888--1899.

Fuk98
Fukushima T. (1998) Symmetric multistep methods revisited. In Proceedings of the 30th symposium on celestial mechanics, pages 229+.

Fuk99
Fukushima T. (1999) Symmetric multistep methods revisited: Ii. numerical experiments. In Evolution and source regions of asteroids and comets : proceedings of the 173rd colloquium of the International Astronomical Union, held in Tatranska Lomnica, Slovak Republic, August 24-28, 1998 / edited by J. Svoren, E.M. Pittich, H. Rickman. Tatranska Lomnica, Slovak Republic : Astronomical Institute of the Slovak Academy of Sciences, 1999., p.309, pages 309+.

GR87
Greengard L. and Rokhlin V. (December 1987) A fast algorithm for particle simulations. Journal of Computational Physics 73: 325--348.

GR88
Greengard L. and Rokhlin V. (1988) Rapid evaluation of potential fields in three dimensions. In Anderson C. and C. A. B. (eds) Vortex Methods, number 1360 in Lecture Notes in Mathematics,, pages 121--141. Springer-Verlag, Berlin.

GR97
Greengard L. and Rokhlin V. (1997) A new version of the fast multipole method for the laplace equation in three dimensions. Acta Numerica 6: 229.

GS86
Gurzadian V. G. and Savvidy G. K. (May 1986) Collective relaxation of stellar systems. 160: 203--210.

Heg74
Heggie D. C. (1974) A global regularisation of the gravitational n-body problem. Celestial Mechanics 10: 217--241.

Hen75
Henon M. (1975) Two recent developments concerning the monte carlo method. In Dynamics of stellar systems, pages 133--149. D. Reidel Publishing Co., Dordrecht.

HHM93
Hernquist L., Hut P., and Makino J. (1993) Discreteness noise versus force errors in n-body simulations. 402: L85--+.

HK89
Hernquist L. and Katz N. (1989) Treesph -- a unification of sph with the hierarchical tree method. 70: 419--446.

HMM95
Hut P., Makino J., and McMillan S. (1995) Building a better leapfrog. 443: L93--L96.

HNNS78
Hachisu I., Nakada Y., Nomoto K., and Sugimoto D. (1978) Gravothermal catastrophe of finite amplitude. Progess of Theoretical Physics 60: 393--402.

HO92
Hernquist L. and Ostriker J. P. (1992) A self-consistent field method for galactic dynamics. 386: 375--397.

HS78
Hachisu I. and Sugimoto D. (1978) Gravothermal catastrophe and negative specific head of self-gravitating systems. Progess of Theoretical Physics 60: 123--135.

HS96
Hardin R. H. and Sloane N. J. A. (1996) Mclaren's improved snub cube and other new spherical designs in three dimensions,. Discrete and Computational Geometry 15: 429--441.

KFM99
Kawai A., Fukushige T., and Makino J. (1999) $9.9/mflops astrophysical n-body simulation with treecode on grape-5. submitted to SC99.

KFMT00
Kawai A., Fukushige T., Makino J., and Taiji M. (August 2000) Grape-5: A special-purpose computer for n-body simulations. 52: 659--676.

KM01
Kawai A. and Makino J. (2001) Pseudoparticle multipole method: A simple method to implement high-accuracy treecode. ASTRO-PH 0012041: --.

KN96
Kinoshita H. and Nakai H. (1996) Long-term behavior of the motion of pluto over 5.5 billion years. Earth Moon and Planets 72: 165--173.

KS65
Kustaanheimo P. and Stiefel E. (1965) Perturbation theory of kepler motion based on spinor regularization. J. Reine. Angew. Math. 218: 204--219.

KYM98
Kokubo E., Yoshinaga K., and Makino J. (July 1998) On a time-symmetric hermite integrator for planetary n-body simulation. 297: 1067--1072.

LE80
Lynden-Bell D. and Eggleton P. P. (1980) On the consequences of the gravothermal catastrophe. 191: 483--498.

Lev06
Levi Civita T. (1906) Sur la r'esolution qualitative probl`eme des trois corps. Acta Math. 30: 305.

LW68
Lynden-Bell D. and Wood R. (1968) The gravo-thermal catastrophe in isothermal spheres and the onset of red-giant structure for stellar systems. 138: 495--525.

MA92
Makino J. and Aarseth S. J. (1992) On a hermite integrator with ahmad-cohen scheme for gravitational many-body problems. 44: 141--151.

MA93a
McMillan S. L. W. and Aarseth S. J. (1993) An o(n log n) integration scheme for collisional stellar systems. 414: 200--212.

MA93b
Mikkola S. and Aarseth S. J. (1993) An implementation of n-body chain regularization. Celestial Mechanics and Dynamical Astronomy 57: 439--459.

MA96
Mikkola S. and Aarseth S. J. (1996) A slow-down treatment for close binaries. Celestial Mechanics and Dynamical Astronomy, v. 64, Issue 3, p. 197-208. 64: 197--208.

Mak90
Makino J. (1990) Vectorization of a treecode. Journal of Computational Physics 87: 148--160.

Mak91a
Makino J. (1991) A modified aarseth code for grape and vector processors. 43: 859--876.

Mak91b
Makino J. (1991) Optimal order and time-step criterion for aarseth-type n-body integrators. 369: 200--212.

Mak97
Makino J. (1997) Merging of galaxies with central black holes. ii. evolution of the black hole binary and the structure of the core. 478: 58+.

Mak99
Makino J. (1999) Yet another fast multipole method without multipoles --- pseudo-particle multipole method. Journal of Computational Physics 151: 910--920.

McL63
McLaren A. D. (1963) Optimal numerical integration on a sphere. Math. Comput. 17: 361--383.

McM86
McMillan S. L. W. (1986) The vectorization of small-n integrators. In Hut P. and McMillan S. (eds) The Use of Supercomputers in Stellar Dynamics, pages 156--161. Springer, New York.

MH88
Makino J. and Hut P. (1988) Performance analysis of direct n-body calculations. 68: 833--856.

MH91
Makino J. and Hut P. (1991) On core collapse. 383: 181--191.

MIE90
Makino J., Ito T., and Ebisuzaki T. (1990) Error analysis of the grape-1 special-purpose n-body machine. 42: 717--736.

MT98
Makino J. and Taiji M. (1998) Scientific Simulations with Special-Purpose Computers --- The GRAPE Systems. John Wiley and Sons, Chichester.

MTES97
Makino J., Taiji M., Ebisuzaki T., and Sugimoto D. (1997) Grape-4: A massively parallel special-purpose computer for collisional n-body simulations. 480: 432--446.

PMHM01
Portegies Zwart S. F., McMillan S. L. W., Hut P., and Makino J. (February 2001) Star cluster ecology - iv. dissection of an open star cluster: photometry. 321: 199+.

PMMH99
Portegies Zwart S. F., Makino J., McMillan S. L. W., and Hut P. (August 1999) Star cluster ecology. iii. runaway collisions in young compact star clusters. 348: 117--126.

QKSL97
Quinn T., Katz N., Stadel J., and Lake G. (1997) Time stepping n-body simulations. ASTRO-PH 9710043: --.

QT90
Quinlan G. D. and Tremaine S. (1990) Symmetric multistep methods for the numerical integration of planetary orbits. 100: 1694--1700.

SaSDW00
Springel V. and ane Simon D.M. White N. Y. (2000) Gadget: A code for collisionless and gasdynamical cosmological simulations. ASTRO-PH 0003162: --.

SB83
Sugimoto D. and Bettwieser E. (1983) Post-collapse evolution of globular clusters. 204: 19P--22P.

SB94
Skeel R. D. and Biesiadecki J. J. (1994) Symplectic integration with variable stepsize. Annals of Numer. Math. 1: 191--198.

SB99
Spurzem R. and Baumgardt H. (1999) A parallel implementation of an aarseth n-body integrator on general and special purpose supercomputers. submitted to .

SG92
Skeel R. D. and Gear C. W. (1992) Does variable step size ruin a symplectic integrator? Physica D 60: 311--313.

Spi56
Spitzer Lyman J. (1956) Physics of Fully Ionized Gases. John Wiley and Sons, Chichester.

Spi87
Spitzer Lyman J. (1987) Dynamical Evolution of Globular Clusters. Princeton University Press, Princeton, New Jersey.

SSC94
Sanz-Serna J. M. and Calvo M. P. (1994) Numerical Hamiltonian Problems. Chapman and Hall, London.

SW88
Sussman G. J. and Wisdom J. (1988) Numerical evidence that the motion of pluto is chaotic. Science 241: 433--437.

Tan87
Tanekusa J. (1987) Statistical theory of violent relaxation. 39: 425--436.

TG00
Tsuchiya T. and Gouda N. (January 2000) Relaxation and lyapunov time scales in a one-dimensional gravitating sheet system. 61: 948--951.

TGK96
Tsuchiya T., Gouda N., and Konishi T. (March 1996) Relaxation processes in one-dimensional self-gravitating many-body systems. 53: 2210--2216.

Vil82
Villumsen J. V. (May 1982) Simulations of galaxy mergers. 199: 493--516.

WGL+98
Warren M. S., Germann T. C., Lomdahl P. S., Beazley D. M., and Salmon J. K. (1998) An alpha/linux cluster achieves 10 gflops for $150k. In Proceedings of SC98, pages (CD--ROM). ACM.

WH91
Wisdom J. and Holman M. (1991) Symplectic maps for the n-body problem. 102: 1528--1538.

WHG96
White C. A. and Head-Gordon M. (1996) Rotating around the quartic angular momentum barrier in fast multipole method calculations. J. Chem. Phys. 105: 22--28.

WOT+95
Woo S. C., Ohara M., Torrie E., Singh J. P., and Gupta A. (1995) The splash-2 programs: Characterization and methodological considerations. In Proceedings of the 22nd International Symposium on Computer Architecture, pages 24--36. ACM.

WS92
Warren M. S. and Salmon J. K. (1992) Astrophysical N-body simulations using hierarchical tree data structures. In Supercomputing '92, pages 570--576. IEEE Comp. Soc., Los Alamitos.

Yos95
吉田春夫. (1995) シンプレクティック数値解法. 数理科学384:.


Jun Makino
Sat Feb 24 22:13:53 JST 2001