Skip to main content Accessibility help
×
Hostname: page-component-797576ffbb-k7d4m Total loading time: 0 Render date: 2023-12-10T21:37:56.833Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

12 - A brief review of other methods of computer simulation

Published online by Cambridge University Press:  24 November 2021

David Landau
Affiliation:
University of Georgia
Kurt Binder
Affiliation:
Johannes Gutenberg Universität Mainz, Germany
Get access

Summary

In the previous chapters of this text we have examined a wide variety of Monte Carlo methods in depth. Although these are exceedingly useful for many different problems in statistical physics, there are some circumstances in which the systems of interest are not well suited to Monte Carlo study. Indeed there are some problems which may not be treatable by stochastic methods at all, since the time-dependent properties as constrained by deterministic equations of motion are the subject of the study. The purpose of this chapter is thus to provide a very brief overview of some of the other important simulation techniques in statistical physics. Our goal is not to present a complete list of other methods or even a thorough discussion of these methods which are included, but rather to offer sufficient background to enable the reader to compare some of the different approaches and better understand the strengths and limitations of Monte Carlo simulations.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abraham, F. F. (1996), Phys. Rev. Lett. 77, 869.CrossRefGoogle Scholar
Abraham, F. F. (2000), Int. J. Mod. Phys. C 11, 1135.CrossRefGoogle Scholar
Agarwal, A. and Delle-Site, L. (2015), J. Chem. Phys. 143, 094102.CrossRefGoogle Scholar
Alder, B. J. and Wainwright, T. E. (1970), Phys. Rev. A 1, 18.CrossRefGoogle Scholar
Allen, M. P. and Tildesley, D. J. (2017), Computer Simulation of Liquids, 2nd ed. (Clarendon Press, Oxford).CrossRefGoogle Scholar
Andersen, H. C. (1980), J. Chem. Phys. 72, 2384.CrossRefGoogle Scholar
Baschnagel, J., Binder, K., Doruker, P., Gusev, A. A., Hahn, O., Kremer, K., Mattice, W. L., Müller-Plathe, F., Murat, M., Paul, W., Santos, S., Suter, U. W., and Tries, V. (2000), Adv. Polymer Sci. 152, 41.CrossRefGoogle Scholar
Beazley, D. M. and Lomdahl, F. S. (1994), Parallel Computing 20, 173.CrossRefGoogle Scholar
Bellman, R. (1957), Dynamic Programming (Princeton University Press, Princeton)Google ScholarPubMed
Berendsen, H. J. C. and Van Gunsteren, W. F. (1986), in Molecular Dynamics Simulation of Statistical Mechanical Systems, Proceedings of the Enrico Fermi Summer School, Varenna (Soc. Italiana di Fisica, Bologna).Google Scholar
Brandt, A., Bernholc, J., and Binder, K. (eds.) (2001), Multiscale Simulations in Physics and Chemistry (IOS Press, Amsterdam).Google Scholar
Bunker, A. and Landau, D. P. (2000), Phys. Rev. Lett. 85, 2601.CrossRefGoogle Scholar
Burden, R. L., Faires, J. D., and Reynolds, A. C. (1981), Numerical Analysis (Prindle, Weber, and Schmidt, Boston).Google Scholar
Bussi, G. and Parrinello, M. (2007), Phys. Rev. E 75, 056707.CrossRefGoogle Scholar
Bussi, G., Donadio, D., and Parrinello, M. (2007), J. Chem. Phys. 126, 014101.CrossRefGoogle Scholar
Car, R. and Parrinello, M. (1985), Phys. Rev. Lett. 55, 2471.CrossRefGoogle Scholar
Carrasquilla, J., and Melko, R. G. (2017), Nature Physics 13, 431.CrossRefGoogle Scholar
Chen, K. and Landau, D. P. (1994), Phys. Rev. B 49, 3266.CrossRefGoogle Scholar
Das, S. K. (2017), J. Chem. Phys. 146, 044902.CrossRefGoogle Scholar
Delgado-Buscalioni, R., Kremer, K., and Prapotnik, M. (2008), J. Chem. Phys. 128, 114110.CrossRefGoogle Scholar
Delgado-Buscalioni, R., Sallic, J., and Prapotnik, M. (2015), Euro. J. Special Topics 224, 42331.Google Scholar
Delle Site, L. and Prapotnik, M. (2017), Phys. Rep. 693, 1.CrossRefGoogle Scholar
d’Humières, D., Pomeau, Y., and Lallemand, P. (1985), C. R. Acad. Sci. II 301, 1391.Google Scholar
Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. (1987), Phys. Lett. B 195, 216.CrossRefGoogle Scholar
Espanol, P. (1995), Phys. Rev. E 52, 1736.CrossRefGoogle Scholar
Espanol, P. and Warren, P. (1995), Europhys. Lett. 19, 155.Google Scholar
Evans, D. J. and Morriss, G. P. (1984), Comput. Phys. Rep. 1, 297.CrossRefGoogle Scholar
Evans, D. J. and Morriss, G. P. (2008), Statistical Mechanics of Nonequilibrium Liquids, 2nd ed. (Cambridge University Press, Cambridge).CrossRefGoogle Scholar
Everitt, B. S., Landau, S., Leese, M., and Stahl, D. (2010), Cluster Analysis (Wiley, Hoboken).Google Scholar
Evertz, H. G. and Landau, D. P. (1996), Phys. Rev. B 54, 12302.CrossRefGoogle Scholar
Frisch, U., Hasslacher, B., and Pomeau, Y. (1986), Phys. Rev. Lett. 56, 1505.CrossRefGoogle Scholar
Gerling, R. W. and Landau, D. P. (1984), J. Magn. Mag. Mat. 45, 267.CrossRefGoogle Scholar
Gilbert, T. L. (1955), Phys. Rev. 100, 1243.Google Scholar
Girard, S. and Müller-Plathe, F. (2004), in Novel Methods in Soft Matter Simulations, eds. Karttunen, M., Vattulainen, I., and Lukkarinen, A. (Springer, Berlin), p. 327.CrossRefGoogle Scholar
Goodfellow, I., Bengio, Y., and Courville, A. (2016), Deep Learning (MIT Press, Boston).Google Scholar
Gompper, G., Ihle, T., Kroll, D. M., and Winkler, R. G. (2009), Adv. Polym. Sci. 221, 1.Google Scholar
Grest, G. S. and Kremer, K. (1986), Phys. Rev. A 33, 3628.CrossRefGoogle Scholar
Grinstein, G. and Koch, R. H. (2003), Phys. Rev. Lett. 90, 207201.CrossRefGoogle Scholar
Groot, R. D. (2004), in Novel Methods in Soft Matter Simulations, eds. Karttunen, M., Vattulainen, I., and Lukkarinen, A. (Springer, Berlin), p. 5.CrossRefGoogle Scholar
Groot, R. D. and Warren, P. (1997), J. Chem. Phys. 107, 4423.CrossRefGoogle Scholar
Hoogerbrugge, P. J. and Koelman, J. M. V. A. (1992), Europhy. Lett. 19, 155.CrossRefGoogle Scholar
Hoover, W. G. (1985), Phys. Rev. A 31, 1695.CrossRefGoogle Scholar
Horbach, J. and Succi, S. (2006), Phys. Rev. Lett. 96, 224 503.CrossRefGoogle Scholar
Ismagilov, R. F., Schwartz, A., Bowden, N., and Whitesides, C. M. (2002), Angew. Chem. Int. Ed. 41, 652.3.0.CO;2-U>CrossRefGoogle Scholar
Jollifee, I. (2002), Principal Component Analysis (Wiley, Chichester)Google Scholar
Kadau, K., Germann, T. C., and Lomdahl, P. S. (2004), Int. J. Mod. Phys. C 15, 193.CrossRefGoogle Scholar
Kalinin, S. V., Sumpter, B. G., and Archibald, R. K. (2015), Nat. Mater. 14, 973.CrossRefGoogle Scholar
Karttunen, M., Vattulainen, D., and Lukkarinen, A. (eds.) (2004), Novel Methods in Soft Matter Simulations (Springer, Berlin).CrossRefGoogle Scholar
Kendon, V. M., Cates, M. E., Pagonabarraga, I., Desplat, J. C., and Bladon, P. (2001), J. Fluid Mech. 440, 147.CrossRefGoogle Scholar
Krech, M., Bunker, A., and Landau, D. P. (1998), Comput. Phys. Commun. 111, 1.CrossRefGoogle Scholar
Laio, A. and Parrinello, M. (2002), Proc. Natl Acad. Sci. USA 99, 562.CrossRefGoogle Scholar
Laio, A. and Parrinello, M. (2006), in Computer Simulations in Condensed Matter: From Materials to Chemical Biology, eds. Ferrario, M., Ciccotti, G., and Binder, K (Springer, Heidelberg), vol. 1, p. 315.Google Scholar
Landau, L. D. and Lifshitz, E. M. (1935), Phys. Z. Sowjetunion 8, 153.Google Scholar
Levin, M., and Wen, X.-G. (2006), Phys. Rev. Lett. 96, 110405.CrossRefGoogle Scholar
Ma, P.-W. and Dudarev, S. L. (2012) Phys. Rev. B 86, 054416.CrossRefGoogle Scholar
Malevanets, A. and Kapral, R. (1999), J. Chem. Phys. 110, 8605.CrossRefGoogle Scholar
Malevanets, A. and Kapral, R. (2000), J. Chem. Phys. 112, 7260.CrossRefGoogle Scholar
Marx, D. and Hutter, J. (2012), Ab initio Molecular Dynamics: Basic Theory and Advanced Methods (Cambridge University Press, Cambridge).Google Scholar
Milchev, A. and Binder, K. (2017), NanoLett. 13, 4324.Google Scholar
Mitra, E. D., Whitehead, S. C., Holowka, D., Baird, B., and Sethna, J. P. (2018), J. Phys. Chem. B 122, 3500.CrossRefGoogle Scholar
Murat, M. and Kremer, K. (1998), J. Chem. Phys. 108, 4340.CrossRefGoogle Scholar
Nelson, D. R. and Fisher, D. S. (1977), Phys. Rev. B 16, 4945.CrossRefGoogle Scholar
Nosé, S. (1984), Mol. Phys. 52, 255.CrossRefGoogle Scholar
Oono, Y. and Puri, S. (1988), Phys. Rev. A 38, 434.CrossRefGoogle Scholar
Palmer, J. C., Haji-Akbari, A., Singh, R. S., Martelli, F., Car, R., Panagiotopoulos, A. Z., and Debenedetti, P. G. (2018), J. Chem. Phys. 148, 137101.CrossRefGoogle ScholarPubMed
Parrinello, M. (1997), Solid State Commun. 102, 107.CrossRefGoogle Scholar
Pastorino, C., Kreer, T., Müller, M., and Binder, K. (2007), Phys. Rev. E 76, 026 706.CrossRefGoogle Scholar
Paul, W., Binder, K., Kremer, K., and Heermann, D. W. (1991), Macromolecules 24, 6332.CrossRefGoogle Scholar
Perera, D., Landau, D. P., Nicholson, D. M., Stocks, G. M., Eisenbach, M., Yin, J., and Brown, G. (2014), J. Appl. Phys. 115, 17D124.CrossRefGoogle Scholar
Perera, D., Nicholson, D. M., Eisenbach, M., Stocks, G. M., and Landau, D. P., (2017), Phys. Rev. B 95, 014431.CrossRefGoogle Scholar
Peruani, F., Starruß, J., Jakovljevic, V., Søgaard-Andersen, L., Deutsch, A., and Bär, M. (2012), Phys. Rev. Lett. 108, 098102.CrossRefGoogle Scholar
Prapotnik, M., Delle Site, L., and Kremer, K. (2008), Ann. Rev. Phys. Chem. 59, 545.CrossRefGoogle Scholar
Rapaport, D. C. (1988), Phys. Rev. Lett. 60, 2480.CrossRefGoogle Scholar
Rapaport, D. C. (2004), The Art of Molecular Dynamics Simulation, 2nd ed. (Cambridge University Press, Cambridge).CrossRefGoogle Scholar
Roth, J., Gähler, F., and Trebin, H.-R. (2000), Int. J. Mod. Phys. C 11, 317.Google Scholar
Rothlisberger, U. and Carloni, P. (2006) in Computer Simulations in Condensed Matter: From Materials to Chemical Biology, eds. Ferrario, M., Ciccotti, G., and Binder, K (Springer, Heidelberg), vol. 2, p. 449.Google Scholar
Rothman, D. H. and Zaleski, S. (1994), Rev. Mod. Phys. 66, 1417.CrossRefGoogle Scholar
Rovere, M., Nielaba, P., and Binder, K. (1993), Z. Physik B-Condensed Matter 90, 215.CrossRefGoogle Scholar
Saitta, L., Giordana, A., and Cornuejols, A. (2011), Phase Transitions in Machine Learning (Cambridge University Press, Cambridge).CrossRefGoogle Scholar
Schneider, T. and Stoll, E. (1978), Phys. Rev. 17, 1302.CrossRefGoogle Scholar
Schweika, W., Maleyev, S. V., Brückel, T., Plakhty, V. P., and Regnault, L.-P. (2002), Europhys. Lett. 69, 446.CrossRefGoogle Scholar
Sidky, H., and Whitmer, J. K. (2018) J. Chem. Phys. 148, 104111.CrossRefGoogle Scholar
Siebert, J. T., Dittrich, F., Schmid, F., Binder, K., Speck, T., and Virnau, P. (2018), Phys. Rev. E 98, 030601.CrossRefGoogle Scholar
Siebert, J. T., Letz, J., Speck, T., and Virnau, P. (2017), Soft Matter 13, 1020.CrossRefGoogle Scholar
Snook, I. (2007), The Langevin and Generalized Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems (Elsevier, Amsterdam).Google Scholar
Succi, S. (2013), The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond (Oxford University Press, Oxford).Google Scholar
Tavazza, F., Nurminen, L., Landau, D. P., Kuronen, A., and Kaski, K. (2004), Phys. Rev. B 70, 184103.CrossRefGoogle Scholar
Tsai, S.-H. and Landau, D. P. (2003), Phys. Rev. B 67, 104411.CrossRefGoogle Scholar
Tsai, S.-H., Bunker, A., and Landau, D. P. (2000), Phys. Rev. B 61, 333.CrossRefGoogle Scholar
Tschöp, W., Kremer, K., Batoulis, J., Bürger, T., and Hahn, O. (1998a), Acta Polymer 49, 61.3.0.CO;2-V>CrossRefGoogle Scholar
Tschöp, W., Kremer, K., Batoulis, J., Bürger, T., and Hahn, O. (1998b), Acta Polymer 49, 75.3.0.CO;2-5>CrossRefGoogle Scholar
Tuckerman, M., Martyna, G. J., and Berne, B. J. (1992), J. Chem. Phys. 97, 1990.CrossRefGoogle Scholar
Verlet, L. (1967), Phys. Rev. 159, 98.CrossRefGoogle Scholar
Verlet, L. (1968), Phys. Rev. 165, 201.CrossRefGoogle Scholar
Vicsek, T., Czirak, A., Ben-Jacob, E., Cohen, I, and Shochet, O. (1995), Phys. Rev. Lett. 75, 1226.CrossRefGoogle Scholar
Villain, J. (1974), J. Phys. (Paris) 35, 27.CrossRefGoogle Scholar
Voter, A. F. (1997), Phys. Rev. Lett. 78, 3908.CrossRefGoogle Scholar
Wang, L. (2016), Phys. Rev. B 94, 195105.CrossRefGoogle Scholar
Whitmer, J. K. and Luijten, E. (2010), J. Phys.: Condens. Matter 22, 104106.Google Scholar
Winkler, A., Virnau, P., Binder, K., Winkler, R. G., and Gompper, G. (2013), J. Chem. Phys. 138, 054901.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×