From Brownian motion to molecular simulations

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dc.citation.epage107
dc.citation.issue2
dc.citation.spage099
dc.contributor.affiliationЛьвівський національний університет імені Івана Франка
dc.contributor.affiliationІнститут фізики конденсованих систем НАН України
dc.contributor.affiliationIvan Franko National University of Lviv
dc.contributor.affiliationInstitute for Condensed Matter Physics of the National Academy of Sciences of Ukraine
dc.contributor.authorРовенчак, А.
dc.contributor.authorТрохимчук, А.
dc.contributor.authorRovenchak, A.
dc.contributor.authorTrokhymchuk, A.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2020-02-27T08:51:42Z
dc.date.available2020-02-27T08:51:42Z
dc.date.created2018-02-26
dc.date.issued2018-02-26
dc.description.abstractНаведено короткий історичний огляд про внесок двох всесвітньо відомих львівських наукових дослідників — Маріана Смолуховського та Станіслава Улама — у розвиток сучасних галузей фізичної науки, таких як молекулярне моделювання, комп’ютерний експеримент та молекулярна інженерія, висвітлено їх зв’язок із останніми дослідженнями, проведеними у львівських університетах та науково-дослідних установах.
dc.description.abstractA brief historical overview towards the contribution of two famous Lviv scholars – Marian Smoluchowski and Stanis law Ulam – to the development of modern physical science fields such as molecular modeling and computer simulations is presented and discussed in connection with recent studies carried out in Lviv universities and research institutions.
dc.format.extent099-107
dc.format.pages9
dc.identifier.citationRovenchak A. From Brownian motion to molecular simulations / A. Rovenchak, A. Trokhymchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 5. — No 2. — P. 099–107.
dc.identifier.citationenRovenchak A. From Brownian motion to molecular simulations / A. Rovenchak, A. Trokhymchuk // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 5. — No 2. — P. 099–107.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/46126
dc.language.isoen
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 2 (5), 2018
dc.relation.references1. Ingen-Housz J. Bemerkungen ¨uber den Gebrauch des Vergr¨osserungsglases. In: Vermischte Schriften physisch-medicinischen Inhalts. Uibersetzt und herausgegeben von Nicolaus Carl Molitor. Zweyter Band. Wien: Christian Friderich Wappler (1784), S. 121–126 (in German).
dc.relation.references2. Brown R. A brief account of microscopical observations made on the particles contained in the pollen of plants. London and Edinburgh Phil. Mag. J. Sci. 4 (21), 161–173 (1828).
dc.relation.references3. Mazo R. M. Brownian Motion. Fluctuations, Dynamics, and Applications. Oxford, Clarendon Press (2002).
dc.relation.references4. PohlW. G. The theory of Brownian motion — one hundred years old. In: The Global and the Local: The History of Science and the Cultural Integration of Europe, Proceedings of the 2nd International Conference of the European Society for the History of Science (Cracow, 2006), edited by M. Kokowski. The Press of the Polish Academy of Arts and Sciences, Cracow (2007), p. 419–424.
dc.relation.references5. https://www.physik.uni-augsburg.de/theo1/hanggi/History/BM-History.html.
dc.relation.references6. Perrin J. La loi de Stokes et le mouvement brownien. C. R. Acad. Sci. Paris. 147, 475-476 (1908); idem, L’origine de mouvement brownien. C. R. Acad. Sci. Paris. 147, 530–533 (1908), (in French).
dc.relation.references7. Einstein A. Uber die von der molekularkinetischen Theorie der W¨arme geforderte Bewegung von in ruhen- ¨ den Fl¨ussigkeiten suspendierten Teilchen. Ann. Phys. 322 (8), 549–560 (1905), (in German).
dc.relation.references8. von Smoluchowski M. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. Phys. 326 (14), 756–780 (1906).
dc.relation.references9. Badino M. Probability and Statistic in Boltzmann’s Early Papers on Kinetic Theory. Dublin Core, Chicago (2006).
dc.relation.references10. Metropolis N., Rosenbluth A. V., Rosenbluth M. N., Teller A. H., Teller E. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 21 (6), 1087–1092 (1953).
dc.relation.references11. von Smoluchowski M. Akustische Untersuchungen ¨uber die Elasticit¨at weicher K¨orper. Sitzungsber. kaiserl. Akad. Wiss. Wien. Math.-naturwiss. Kl. 103 (II.a), 739–72 (1894), (in German).
dc.relation.references12. Montroll E.W. On the Vienna School of statistical thought. AIP Conference Proceedings. 109 (1), 1–10 (1984).
dc.relation.references13. Rovenchak A. Lviv period for Smoluchowski: Science, teaching, and beyond. Condens. Matter Phys. 15 (4), 40002 (2012).
dc.relation.references14. Mehra J., Rechenberg H. The Historical Development of Quantum Theory. Vol. 5. Springer (2001).
dc.relation.references15. Coen D. R. Vienna in the Age of Uncertainty: Science, Liberalism, and Private Life. University of Chicago Press (2007).
dc.relation.references16. Teske A. Marian Smoluchowski: ˙zycie i tw´orczo´s´c. PWN, Krak´ow, 1955 (in Polish); German translation: Teske A., Marian Smoluchowski: Leben und Werk, Wroc law–Warszawa–Krak´ow–Gda´nsk, 1977.
dc.relation.references17. G´ora P. E. Fluktuacje wok´o l nas. Dziedzictwo Mariana Smoluchowskiego. PAUza Akademicka. Tygodnik Polskiej Akademii Umieje˛tno´sci. 9 (380–381), 4–5 (2017).
dc.relation.references18. Ulam S. Marian Smoluchowski and the theory of probabilities in physics. Am. J. Phys. 25 (7), 475–481 (1957).
dc.relation.references19. SzymanskiW.W., Posch H. A. Marian Wilhelm Theofil von Smoluchowski. http://www.iara.org/ AerosolPioneers.htm
dc.relation.references20. http://ktf.lnu.edu.ua/cgi-bin/KTF/select.cgi?Smoluchowski
dc.relation.references21. Hoborski A. Prof. dr Jan Stock wspomnienie po´smiertne. Przegla˛d G´orniczo-Hutniczy. 27, 454–457 (1925), (in Polish).
dc.relation.references22. Rovenchak A. Department for Experimental Physics, University of Lviv, in 1872–1939: Contributions to biobibliography. J. Phys. Stud. 22 (4), 4002 (2018).
dc.relation.references23. Smoluchowski M. Zarys teoryi kinetycznej ruch´ow Browna i roztwor´ow me˛tnych. Rozpr. Wydz. matem.- przyrodn. Ak. Umieje˛t. Ser. III 6A, 257–281 (1906), (in Polish).
dc.relation.references24. Smoluchowski M. Essai d’une th´eorie cin´etique du muovement Brownien et des milieux troubles. Bull. Int. Acad. Sci. Cracovie. Cl. sci. math. nat. 577–602 (1906), (in French).
dc.relation.references25. Bodaszewsky L. J. Rauch und Dampf unter dem Mikroskop. Dinglers Polytechn. J. 239, 324–325 (1881), (in German).
dc.relation.references26. Kozhushko B. V., Shenderovskyj V. A. Zabute v nauci im’ja (Lukash Bodashevskyj — fizyk i hidromekhanik). Visnyk Nacionalnoho Tekhnichnoho Universytetu “KhPI”. 64, 71–76 (2011), (in Ukrainian).
dc.relation.references27. Wr´oblewski A. K. Polish physicists and the progress in physics (1870–1920). Techn. Trans. Fund. Sci. 111 (1), 255–273 (2014).
dc.relation.references28. Mehra J. Golden Age Of Theoretical Physics. Vol. 1. World Scientific (2001).
dc.relation.references29. Smoluchowski M. Versuch einer mathematischen Theorie der Koagulationskinetic kolloider L¨osungen. Z. Phys. Chem. 92U (1), 129–168 (1917), (in German).
dc.relation.references30. Smoluchowski M. Grundriß der Koagulationskinetik kolloider L¨osungen. Kolloid-Zeitschrift. 21, 98–104 (1917), (in German).
dc.relation.references31. Mycielski J. Stanis law Marcin Ulam (1909–1984). Rocz. Pol. Tow. Matem. Ser. II: Wiad. Matem. 29, 21–37 (1990), (in Polish).
dc.relation.references32. Program Politechniki Lwowskiej na rok akademicki 1933/34. Lw´ow, 1933 (in Polish).
dc.relation.references33. Ponedilok G. V., Rovenchak A. A. To the history of theoretical physics studies at the Lviv Polytechnic. J. Phys. Stud. 21, 1003 (2017).
dc.relation.references34. Bazylevych L., Guran I., Zarichnyi M. Lw´ow period of S. Ulam’s mathematical creativity. Techn. Trans. Fund. Sci. 2-NP, 33–39 (2015).
dc.relation.references35. Ulam S. Adventures of a Mathematician. University of California Press (1976).
dc.relation.references36. Eckhardt R. Stan Ulam, John von Neumann, and the Monte Carlo Method. In: From Cardinals to Chaos: Reflections on the life and legacy of Stanislaw Ulam. Cambridge, Cambridge University Press (1989). First published in Los Alamos Science Special Issue, 131–141 (1987); https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-88-9068.
dc.relation.references37. Giesler G. C. MCNP software quality: Then and now. Los Alamos National Laboratory Report LA-UR-00-2532 (2000); https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/ LA-UR-00-2532.
dc.relation.references38. Gass S. I., Assad A. A. Model World: Tales from the Time Line—The Definition of OR and the Origins of Monte Carlo Simulation. Interfaces. 35 (5), 429–435 (2005).
dc.relation.references39. Allen M. P., Tildesley D. J. Computer Simulation of Liquids. New York, Oxford University Press (2002).
dc.relation.references40. Frenkel D., Smit B. Understanding Molecular Simulation: From Algorithms to Applications. 2nd ed. London, Academic Press (2002).
dc.relation.references41. Engel M., Anderson J. A., Glotzer S. C., Isobe M., Bernard E. P., KrauthW. Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods. Phys. Rev. E. 87, 042134 (2013).
dc.relation.references42. Omelyan I. P., Mryglod I. M., Folk R. Construction of high-order force-gradient algorithms for integration of motion in classical and quantum systems. Phys. Rev. E. 66, 026701 (2002).
dc.relation.references43. Omelyan I. P., Mryglod I. M., Folk R. Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. Computer Phys. Commun. 151 (3), 272–314 (2003).
dc.relation.references44. Trokhymchuk A., Alejandre J. Computer simulations of liquid/vapor interface in Lennard–Jones fluids: Some questions and answers. J. Chem. Phys. 111 (18), 8510–8523 (1999).
dc.relation.references45. Simeoni G. G., Bryk T., Gorelli F. A., Krisch M., Ruocco G., Santoro M., Scopigno T. The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids. Nature Phys. 6, 503–507 (2010).
dc.relation.references46. Bryk T., Haymet A. D. J. Ice 1h/water interface of the SPC/E model: Molecular dynamics simulations of the equilibrium basal and prism interfaces. J. Chem. Phys. 117 (22), 10258–10268 (2002).
dc.relation.references47. Wilson M. R., Ilnytskyi J. M., Stimson L. M. Computer simulations of a liquid crystalline dendrimer in liquid crystalline solvents. J. Chem. Phys. 119 (6), 3509–3515 (2003).
dc.relation.references48. Baumketner A., Bernstein S. L., Wyttenbach T., Bitan G., Teplow D. B., Bowers M. T., Shea J. E. Amyloid β-protein monomer structure: A computational and experimental study. Protein Sci. 15 (3), 420–428 (2006).
dc.relation.references49. Smalyukh I., Trokhymchuk A. Planer-Smoluchowski Soft Matter Workshop on Liquid Crystals and Colloidal Dispersions. Condens. Matter Phys. 13 (3), 37101 (2010).
dc.relation.references50. http://www.icmp.lviv.ua/pssm2011.
dc.relation.references51. http://www.icmp.lviv.ua/statphys2012.
dc.relation.references52. http://icmp.lviv.ua/ucsw2017.
dc.relation.referencesen1. Ingen-Housz J. Bemerkungen ¨uber den Gebrauch des Vergr¨osserungsglases. In: Vermischte Schriften physisch-medicinischen Inhalts. Uibersetzt und herausgegeben von Nicolaus Carl Molitor. Zweyter Band. Wien: Christian Friderich Wappler (1784), S. 121–126 (in German).
dc.relation.referencesen2. Brown R. A brief account of microscopical observations made on the particles contained in the pollen of plants. London and Edinburgh Phil. Mag. J. Sci. 4 (21), 161–173 (1828).
dc.relation.referencesen3. Mazo R. M. Brownian Motion. Fluctuations, Dynamics, and Applications. Oxford, Clarendon Press (2002).
dc.relation.referencesen4. PohlW. G. The theory of Brownian motion - one hundred years old. In: The Global and the Local: The History of Science and the Cultural Integration of Europe, Proceedings of the 2nd International Conference of the European Society for the History of Science (Cracow, 2006), edited by M. Kokowski. The Press of the Polish Academy of Arts and Sciences, Cracow (2007), p. 419–424.
dc.relation.referencesen5. https://www.physik.uni-augsburg.de/theo1/hanggi/History/BM-History.html.
dc.relation.referencesen6. Perrin J. La loi de Stokes et le mouvement brownien. C. R. Acad. Sci. Paris. 147, 475-476 (1908); idem, L’origine de mouvement brownien. C. R. Acad. Sci. Paris. 147, 530–533 (1908), (in French).
dc.relation.referencesen7. Einstein A. Uber die von der molekularkinetischen Theorie der W¨arme geforderte Bewegung von in ruhen- ¨ den Fl¨ussigkeiten suspendierten Teilchen. Ann. Phys. 322 (8), 549–560 (1905), (in German).
dc.relation.referencesen8. von Smoluchowski M. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. Phys. 326 (14), 756–780 (1906).
dc.relation.referencesen9. Badino M. Probability and Statistic in Boltzmann’s Early Papers on Kinetic Theory. Dublin Core, Chicago (2006).
dc.relation.referencesen10. Metropolis N., Rosenbluth A. V., Rosenbluth M. N., Teller A. H., Teller E. Equation of State Calculations by Fast Computing Machines. J. Chem. Phys. 21 (6), 1087–1092 (1953).
dc.relation.referencesen11. von Smoluchowski M. Akustische Untersuchungen ¨uber die Elasticit¨at weicher K¨orper. Sitzungsber. kaiserl. Akad. Wiss. Wien. Math.-naturwiss. Kl. 103 (II.a), 739–72 (1894), (in German).
dc.relation.referencesen12. Montroll E.W. On the Vienna School of statistical thought. AIP Conference Proceedings. 109 (1), 1–10 (1984).
dc.relation.referencesen13. Rovenchak A. Lviv period for Smoluchowski: Science, teaching, and beyond. Condens. Matter Phys. 15 (4), 40002 (2012).
dc.relation.referencesen14. Mehra J., Rechenberg H. The Historical Development of Quantum Theory. Vol. 5. Springer (2001).
dc.relation.referencesen15. Coen D. R. Vienna in the Age of Uncertainty: Science, Liberalism, and Private Life. University of Chicago Press (2007).
dc.relation.referencesen16. Teske A. Marian Smoluchowski: ˙zycie i tw´orczo´s´c. PWN, Krak´ow, 1955 (in Polish); German translation: Teske A., Marian Smoluchowski: Leben und Werk, Wroc law–Warszawa–Krak´ow–Gda´nsk, 1977.
dc.relation.referencesen17. G´ora P. E. Fluktuacje wok´o l nas. Dziedzictwo Mariana Smoluchowskiego. PAUza Akademicka. Tygodnik Polskiej Akademii Umieje˛tno´sci. 9 (380–381), 4–5 (2017).
dc.relation.referencesen18. Ulam S. Marian Smoluchowski and the theory of probabilities in physics. Am. J. Phys. 25 (7), 475–481 (1957).
dc.relation.referencesen19. SzymanskiW.W., Posch H. A. Marian Wilhelm Theofil von Smoluchowski. http://www.iara.org/ AerosolPioneers.htm
dc.relation.referencesen20. http://ktf.lnu.edu.ua/cgi-bin/KTF/select.cgi?Smoluchowski
dc.relation.referencesen21. Hoborski A. Prof. dr Jan Stock wspomnienie po´smiertne. Przegla˛d G´orniczo-Hutniczy. 27, 454–457 (1925), (in Polish).
dc.relation.referencesen22. Rovenchak A. Department for Experimental Physics, University of Lviv, in 1872–1939: Contributions to biobibliography. J. Phys. Stud. 22 (4), 4002 (2018).
dc.relation.referencesen23. Smoluchowski M. Zarys teoryi kinetycznej ruch´ow Browna i roztwor´ow me˛tnych. Rozpr. Wydz. matem, przyrodn. Ak. Umieje˛t. Ser. III 6A, 257–281 (1906), (in Polish).
dc.relation.referencesen24. Smoluchowski M. Essai d’une th´eorie cin´etique du muovement Brownien et des milieux troubles. Bull. Int. Acad. Sci. Cracovie. Cl. sci. math. nat. 577–602 (1906), (in French).
dc.relation.referencesen25. Bodaszewsky L. J. Rauch und Dampf unter dem Mikroskop. Dinglers Polytechn. J. 239, 324–325 (1881), (in German).
dc.relation.referencesen26. Kozhushko B. V., Shenderovskyj V. A. Zabute v nauci im’ja (Lukash Bodashevskyj - fizyk i hidromekhanik). Visnyk Nacionalnoho Tekhnichnoho Universytetu "KhPI". 64, 71–76 (2011), (in Ukrainian).
dc.relation.referencesen27. Wr´oblewski A. K. Polish physicists and the progress in physics (1870–1920). Techn. Trans. Fund. Sci. 111 (1), 255–273 (2014).
dc.relation.referencesen28. Mehra J. Golden Age Of Theoretical Physics. Vol. 1. World Scientific (2001).
dc.relation.referencesen29. Smoluchowski M. Versuch einer mathematischen Theorie der Koagulationskinetic kolloider L¨osungen. Z. Phys. Chem. 92U (1), 129–168 (1917), (in German).
dc.relation.referencesen30. Smoluchowski M. Grundriß der Koagulationskinetik kolloider L¨osungen. Kolloid-Zeitschrift. 21, 98–104 (1917), (in German).
dc.relation.referencesen31. Mycielski J. Stanis law Marcin Ulam (1909–1984). Rocz. Pol. Tow. Matem. Ser. II: Wiad. Matem. 29, 21–37 (1990), (in Polish).
dc.relation.referencesen32. Program Politechniki Lwowskiej na rok akademicki 1933/34. Lw´ow, 1933 (in Polish).
dc.relation.referencesen33. Ponedilok G. V., Rovenchak A. A. To the history of theoretical physics studies at the Lviv Polytechnic. J. Phys. Stud. 21, 1003 (2017).
dc.relation.referencesen34. Bazylevych L., Guran I., Zarichnyi M. Lw´ow period of S. Ulam’s mathematical creativity. Techn. Trans. Fund. Sci. 2-NP, 33–39 (2015).
dc.relation.referencesen35. Ulam S. Adventures of a Mathematician. University of California Press (1976).
dc.relation.referencesen36. Eckhardt R. Stan Ulam, John von Neumann, and the Monte Carlo Method. In: From Cardinals to Chaos: Reflections on the life and legacy of Stanislaw Ulam. Cambridge, Cambridge University Press (1989). First published in Los Alamos Science Special Issue, 131–141 (1987); https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-88-9068.
dc.relation.referencesen37. Giesler G. C. MCNP software quality: Then and now. Los Alamos National Laboratory Report LA-UR-00-2532 (2000); https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/ LA-UR-00-2532.
dc.relation.referencesen38. Gass S. I., Assad A. A. Model World: Tales from the Time Line-The Definition of OR and the Origins of Monte Carlo Simulation. Interfaces. 35 (5), 429–435 (2005).
dc.relation.referencesen39. Allen M. P., Tildesley D. J. Computer Simulation of Liquids. New York, Oxford University Press (2002).
dc.relation.referencesen40. Frenkel D., Smit B. Understanding Molecular Simulation: From Algorithms to Applications. 2nd ed. London, Academic Press (2002).
dc.relation.referencesen41. Engel M., Anderson J. A., Glotzer S. C., Isobe M., Bernard E. P., KrauthW. Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods. Phys. Rev. E. 87, 042134 (2013).
dc.relation.referencesen42. Omelyan I. P., Mryglod I. M., Folk R. Construction of high-order force-gradient algorithms for integration of motion in classical and quantum systems. Phys. Rev. E. 66, 026701 (2002).
dc.relation.referencesen43. Omelyan I. P., Mryglod I. M., Folk R. Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. Computer Phys. Commun. 151 (3), 272–314 (2003).
dc.relation.referencesen44. Trokhymchuk A., Alejandre J. Computer simulations of liquid/vapor interface in Lennard–Jones fluids: Some questions and answers. J. Chem. Phys. 111 (18), 8510–8523 (1999).
dc.relation.referencesen45. Simeoni G. G., Bryk T., Gorelli F. A., Krisch M., Ruocco G., Santoro M., Scopigno T. The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids. Nature Phys. 6, 503–507 (2010).
dc.relation.referencesen46. Bryk T., Haymet A. D. J. Ice 1h/water interface of the SPC/E model: Molecular dynamics simulations of the equilibrium basal and prism interfaces. J. Chem. Phys. 117 (22), 10258–10268 (2002).
dc.relation.referencesen47. Wilson M. R., Ilnytskyi J. M., Stimson L. M. Computer simulations of a liquid crystalline dendrimer in liquid crystalline solvents. J. Chem. Phys. 119 (6), 3509–3515 (2003).
dc.relation.referencesen48. Baumketner A., Bernstein S. L., Wyttenbach T., Bitan G., Teplow D. B., Bowers M. T., Shea J. E. Amyloid b-protein monomer structure: A computational and experimental study. Protein Sci. 15 (3), 420–428 (2006).
dc.relation.referencesen49. Smalyukh I., Trokhymchuk A. Planer-Smoluchowski Soft Matter Workshop on Liquid Crystals and Colloidal Dispersions. Condens. Matter Phys. 13 (3), 37101 (2010).
dc.relation.referencesen50. http://www.icmp.lviv.ua/pssm2011.
dc.relation.referencesen51. http://www.icmp.lviv.ua/statphys2012.
dc.relation.referencesen52. http://icmp.lviv.ua/ucsw2017.
dc.relation.urihttps://www.physik.uni-augsburg.de/theo1/hanggi/History/BM-History.html
dc.relation.urihttp://www.iara.org/
dc.relation.urihttp://ktf.lnu.edu.ua/cgi-bin/KTF/select.cgi?Smoluchowski
dc.relation.urihttps://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-88-9068
dc.relation.urihttps://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/
dc.relation.urihttp://www.icmp.lviv.ua/pssm2011
dc.relation.urihttp://www.icmp.lviv.ua/statphys2012
dc.relation.urihttp://icmp.lviv.ua/ucsw2017
dc.rights.holderCMM IAPMM NASU
dc.rights.holder© 2018 Lviv Polytechnic National University
dc.subjectісторія науки
dc.subjectметод Монте-Карло
dc.subjectметод молекулярної динаміки
dc.subjectпершопринципні ab initio симуляції
dc.subjecthistory of science
dc.subjectMonte Carlo simulations
dc.subjectmolecular dynamics simulations
dc.subjectfirst principles ab initio simulations
dc.subject.udc53(091)
dc.subject.udc501
dc.subject.udc533.723
dc.subject.udc544.77
dc.titleFrom Brownian motion to molecular simulations
dc.title.alternativeВід броунівського руху до молекулярного комп’ютерного експерименту
dc.typeArticle

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Mathematical Modeling And Computing. – 2018. – Vol. 5, No. 2