The application simulated modelling in materials science

V. I. Bol'shakov, V. N. Volchuk, Yu. I. Dubrov

Abstract


Formulation of the problem. An important part of the experiment is to obtain a random number sequence with specific characteristics. To simulate any predetermined random process must be able to build enough economical sequence of random numbers corresponding to certain fixed laws of distribution. To obtain the value of the random variable with given distribution, typically use one or more values are uniformly distributed random numbers. Therefore the question of the development of methods for obtaining a uniformly distributed random numbers on a computer has a special meaning, a significant effect on the use of simulation in the practice of solving problems with a large number of variables. Objective. The definition of convergence model with reality. Main part. Model billiard problem allows an experiment aimed at the study of dissipative systems with chaotic layer in the intermediate region, which may occur under certain conditions. At the same time, to give the "most chaotic", in terms of experience has enabled the possibility of job strain sides of billiards by permanent changes in their ellipsoidal, and the constant movement of the balls-reflectors along a predetermined path. The model describing such systems is sensitive to the initial data, and the two close paths over time, which will be removed from each other. As compared to this case, the results of theory and experiment? Small inaccuracies in the determination of the initial state of the system leads to the fact that the difference between the trajectory predicted by theory and experimental data will increase. The reason for this phenomenon is not disadvantages of the model and the nature of the phenomena studied. Conclusions. The way out of this situation is not a comparison of the trajectory of the image point of the object model and at the same times, and some of the more complex characteristics that determine the intrinsic properties of the processes under study.


Keywords


simulated; billiard challenge; random numbers; Monte Carlo; synergetics

References


Чернавский Д. С. Синергетика и информация. Динамическая теория хаоса / Д. С. Чернавский. - Москва : Наука, 2001.- 105 с.

Chernavskiy D. S. Sinergetika i informaciya. Dinamicheskaya teoriya haosa [Synergetics and Information. Dynamic chaos theory]. Moscow: Nauka Publ., 2001, 105 p. (in Russian).

Шеннон К. Работы по теории информации и кибернетике /

К. Шеннон. - Москва : Изд-во иностр. лит., 1963. - 830 с.

Shennon K. Raboty po teorii informacii i kibernetike [Works on information theory and cybernetics]. Moscow : Foreign Lit. Publ., 1963, 830 p. (in Russian).

Бир С. Кибернетика и управление производством / С. Бир. - Москва : Наука, 1963. – 276 с.

Bir S. Kibernetika i upravlenie proizvodstvom [Cybernetics and production management]. Moscow : Nauka Publ., 1963, 276 p. (in Russian).

Колмогоров А. Н. Теория информации и теория алгоритмов /

А. Н. Колмогоров. - Москва : Наука, 1987. - 304 с.

Kolmogorov A. N. Teoriya informacii i teoriya algoritmov [Theory and information theory of algorithms]. Moscow : Nauka Publ., 1987, 304 p. (in Russian).

Журбенко И. Г. Определение критической длины последовательности псевдослучайных чисел / И. Г. Журбенко,

И. А. Кожевникова, О. В. Клиндоухова // Вероятностно-статистические методы исследования. - Москва : Изд-во МГУ, 1983. - С. 18-39.

Zhurbenko I.G., Kozhevnikova I.A. and Klindoukhova O.V. Opredelenie kriticheskoj dliny posledovatel'nosti psevdosluchajnyh chisel [Determination of the critical length of the pseudo-random number]. Veroyatnostno-statisticheskie metody issledovaniya [Probabilistic and statistical research methods]. Moscow : MGU Publ., 1983, pр. 18-39.

(in Russian).

Метод статистических испытаний (метод Монте-Карло) : монография / [Н. П. Бусленко, Д. И. Голенко, И. М. Соболь и др.]. – Москва : Физматгиз, 1962. - 332 с.

Buslenko N.P., Golenko D.I., Sobol' I.M. and etc. Metod statisticheskih ispytanij (metod Monte-Karlo) [Method of statistical tests (Monte Carlo)]. Moscow : Fizmatgiz Publ., 1962, 332 p. (in Russian).

Браун Дж. Методы Монте-Карло [Текст] / Дж. Браун // Современная математика для инженеров. Под ред. Э. Ф. Беккенбаха. – Москва : Изд-во иностр. лит., 1958. – 500 с.

Braun Dzh. Metody Monte-Karlo [Tekst] [Monte Carlo Methods [Text]]. Sovremennaya matematika dlya inzhenerov [Contemporary Mathematics for Engineers]. Edited by E. F. Bekkenbah. Moscow : Foreign Lit. Publ., 1958, 500 p. (in Russian).

Метод статистических испытаний (метод Монте-Карло) и его реализация в цифровых машинах / Н. П. Бусленко, Ю. А. Шрейдер. - Москва : Физматгиз, 1961. - 226 с.

Buslenko N.P. and Shreyder Yu.A. Metod statisticheskih ispytanij (metod Monte-Karlo) i ego realizaciya v cifrovyh mashinah [The method of statistical tests (Monte Carlo) and its implementation in digital machines]. Moscow : Fizmatgiz Publ., 1961, 226 р. (in Russian).

Дубров Ю. И. Исследования имитационной модели «бильярдной задачи», а также ее применение в практике преподавания синергетики / Ю. И. Дубров // Математика. Компьютер. Образование : матер. междунар. науч. конф. [26-31 января, 1998 г., Россия]. - Дубна, 1998. - С. 71–83.

Dubrov Yu.I. Issledovaniya imitatsionnoy modeli «bilyardnoy zadachi», a takzhe ee primenenie v praktike prepodavaniya sinergetiki [Research simulation model "billiard problem", as well as its application in practice of teaching of synergy]. Mathematics. Computer. Education : Mater. Intern. Scientific. Conf., Dubna (Russia), 26-31 of Jan., 1998, рp. 71–83. (in Russian).

Математические бильярды : монография / [А. Н. Земляков,

Г. А. Гальперин]. - Москва : Наука, 1990. - 290 с.

Zemlyakov A.N. and Gal'perin G.A. Matematicheskiye bil'yardy : monografiya [Mathematical billiards : monograph]. Moscow : Science Publ., 1990, 290 p. (in Russian).

Кориолис Г. Г. Математическая теория явлений бильярдной игры / Г. Г. Кориолис. - Москва : Гостехиздат, 1956. – 235 с.

Coriolis G.G. Matematicheskaya teoriya yavlenij bil'yardnoj igry [Mathematical Theory phenomena snooker]. Moscow : Gostekhizdat, 1956, 235 p. (in Russian).

Борахеостов В. Бильярды / В. Борахеостов // Наука и жизнь. - 1966. - №№ 2-4, 6, 11.

Borakheostov V. Bil'yardy [Billiards]. Nauka i zhizn [Science and Life]. 1966, no. 2−4, 6, 11. (in Russian).

Гальперин Г. А. Математические бильярды (бильярдные задачи и смежные вопросы математики и механики) / Г. А. Гальперин,

А. Н. Земляков. - Москва : Наука, 1990. - 288 с.

Gal'perin G.A. and Zemlyakov A.N. Matematicheskiye bil'yardy (bil'yardnyye zadachi i smezhnyye voprosy matematiki i mekhaniki) [Mathematical billiards (billiard problem and related problems of mathematics and mechanics)]. Moscow : Science Publ., 199, 288 р. (in Russian).


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