Стохастические модели взаимодействия

Роль случайностей в разных явлениях различна. В некоторых явлениях случайные отклонения от закономерностей настолько малы, что их можно не учитывать. Однако существуют такие явления, в которых невозможно подметить никаких закономерностей и случайность играет основную роль. Примером такого явления может служить движение малой частицы твердого вещества, взвешенной в жидкости, так называемое броуновское движение. Под действием толчков молекул жидкости частица движется совершенно беспорядочно, без всякой видимой закономерности. При движении индивидуальной частицы сама случайность является закономерностью. Однако если броуновских частиц много, их концентрация в пространстве меняется, подчиняясь определенным закономерностям, происходит диффузия таких частиц из области высоких концентраций в область более низких концентраций. Этот процесс диффузии в некотором приближении можно описывать детерминированной моделью. В детерминированных моделях значение переменных можно точно предсказать.

При исследовании многих процессов в физике, химии, биологии было замечено: в ряде случаев свойством воспроизводимости обладают не сами числовые значения какой-либо переменной, а их распределения — частоты, с которыми значение этой переменной принадлежит тому или иному интервалу на числовой прямой. В таких случаях состояние системы можно описывать распределением вероятностей, а эволюцию системы во времени — эволюцией распределений. Соответствующие модели являются стохастическими.

UNIT 31 X-Ray Diffraction and Molecular Structure

An individual biological molecule typically comprises hundreds or even thousands of atoms, and it is naturally important to know how these are arranged with respect to one another, for it is this arrangement that dictates the molecule's physical behaviour under a given set of conditions. The most straightforward technique for determining the relative positions of the various atoms in a molecule is to consolidate a large number of such molecules into a crystal, that is to say an orderly array in which the individual molecules have identical surroundings (except those at the crystal surface, of course). It will then be the case that the equivalent atoms in the various molecules will themselves be arranged in a crystalline arrangement having the same symmetry as the overall pattern of molecules. The positions of the individual atoms in each and every molecule can then be determined by causing the crystal to diffract X-rays, and by making measurements on the resulting diffraction pattern. However, before considering the details, we should familiarize ourselves with some of the underlying crystallographic principles.

The painstaking cataloguing of the shapes of crystals of numerous chemical compounds, by the early crystallographers, revealed that there are just seven fundamentally different symmetry systems, by which three-dimensional space can be divided up into regular units. These crystal systems range from the cubic system, in which all the angles of the elementary unit are right angles and all the side lengths are equal, to the triclinic system, in which all the angles and all the side lengths are mutually different. Intermediate between these extremes are the tetragonal system, the orthorhombic system, the rhombohedral system, the hexagonal system and the monoclinic system. In 1848, Auguste Bravais established that there are just 14 different ways of arranging identical items so as to fill three-dimensional space in an orderly manner. These are now known as the Bravais lattices, and they are a subdivision of the above-mentioned seven crystal systems. In two dimensions, the number of different possibilities drops to five, and this imposes a fundamental limitation on the available symmetries in wall-paper, for example.

Define the following words using a dictionary

An array, to familiarize oneself with.., painstaking, with respect to, to impose, lattice.

Complete the sentences

1. It is important to know how atoms…
2. It is this arrangement of atoms…
3. The most straightforward technique to determine the relative positions of the atoms in a molecule is …
4. The positions of the individual atoms…
5. before considering the details,...
6. The cataloguing of the shapes of crystals of numerous chemical compounds, revealed that…
7. These crystal systems range…

Match the words from the left column with their synonyms in the right column

Match the words from the two columns to make up collocations. Translate them into Russian.

Translate into Russian

1. Recent work indicates that in micro-organisms mutation rate measured as the frequency of mutation at each gene replication is not affected by temperature. Ryan and Kiritani found the mutation rate of histidine auxotrophy to histidine prototrophy in Escherichia coli to be the same per mutable unit per generation at all temperatures tested.

2. However, respiration deficiency in yeasts seems to depend on the absence of a cytoplasmic particle.

3. This finding in Drosophila would then agree with the work on micro-organisms referred to in the introduction.

4. Sheldon has suggested that mutation observed by previous authors were affected by age of males used.

5. It can be concluded therefore that Sheldon's paper and the present study, unlike the earlier ones, have shown the effect of temperature during development on the spontaneous mutation process. Temperature appears to have no effect on this basal rate, when calculated as mutations per cell generation.

6. The late flies were smaller than the early ones. If this were due to suboptimal nutrition as the cultures aged, then the late flies may have had fewer cells, as reported by Robertson, i. e. may have undergone fewer cell generations.

7. That both these mechanisms are involved in the difference between early and late oocytes cannot be ruled out on present data.

8. However, Child's condition must have involved gross deficiency of essential nutrients, which might be expected to increase the mutation frequency.

9. However, little is known concerning the basis for these large differences in sensitivity to mutagens or whether chemically induced dominant lethals are cytologically similar to those induced by ionizing radiation.

10. Since only low dose rate equipment was available at the start of the studies, 14000 R rather than a higher dose was selected because the higher dose would have required nearly an hour to administer.

11. The latter type appeared as a large deeply staining chromatin mass and was scored as unfertilized.

12. It is difficult to choose between either of these alternatives, although the correct one must certainly affect our interpretation of differential sensitivity of germ-cell stages.

13. According to older ideas about the nature of inheritance we should have expected an «Аа» individual to form gametes which also represented something intermediate between «А» and «а».

14. In this case only one pollen category is normally functional, 50% of the pollen being consequently inactive, though all the pollen grains appear to be normal.

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