Jamming and percolation of parallel squares in single-cluster growth model
This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a square lattice were occupied by addition of the equal size k x k squares (E-problem) or a mixture of...
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| Дата: | 2014 |
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| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2014
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/153448 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Jamming and percolation of parallel squares in single-cluster growth model / I.A. Kriuchevskyi, L.A. Bulavin, Yu.Yu. Tarasevich, N.I. Lebovka // Condensed Matter Physics. — 2014. — Т. 17, № 3. — С. 33006:1-11. — Бібліогр.: 42 назв.— англ. |
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nasplib_isofts_kiev_ua-123456789-1534482025-02-09T11:51:32Z Jamming and percolation of parallel squares in single-cluster growth model Джамiнг та перколяцiя паралельних квадратiв в однокластернiй моделi росту Kriuchevskyi, I.A. Bulavin, L.A. Tarasevich, Yu.Yu. Lebovka, N.I. This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a square lattice were occupied by addition of the equal size k x k squares (E-problem) or a mixture of k x k and m x m (m ≤ k) squares (M-problem). The larger k x k squares were assumed to be active (conductive) and the smaller m x m squares were assumed to be blocked (non-conductive). For equal size k x k squares (E-problem) the value of pj = 0.638 ± 0.001 was obtained for the jamming concentration in the limit of k →∞. This value was noticeably larger than that previously reported for a random sequential adsorption model, pj = 0.564 ± 0.002. It was observed that the value of percolation threshold pc (i.e., the ratio of the area of active k x k squares and the total area of k x k squares in the percolation point) increased with an increase of k. For mixture of k x k and m x m squares (M-problem), the value of pc noticeably increased with an increase of k at a fixed value of m and approached 1 at k ≥ 10 m. This reflects that percolation of larger active squares in M-problem can be effectively suppressed in the presence of smaller blocked squares. В роботi вивчено явища джамiнгу i перколяцiї паралельних квадратiв для однокластерної моделi росту. Для росту кластеру з активного зародку використовувався метод Лiса-Александровича. Вузли квадратної ґратки займалися додаванням однакових k ×k квадратiв (E-задача) або сумiшi k ×k i m ×m (m É k) квадратiв (M-задача). Припускалося, що бiльшi k × k областi були активними (провiдними), а меншi були заблокованими (непровiдними). Для k ×k квадратiв однакового розмiру (E-задача) за умови k → ∞ було отримано таке значення концентрацiї джамiнгу p j = 0.638±0.001 . Це значення було iстотно меншим за отримане ранiше для моделi випадкової послiдовної адсорбцiї: p j = 0.564±0.002. Було показано, що величина перколяцiйного порогу pc (тобто вiдношення площi активних k ×k квадратiв до загальної площi осаджених k × k квадратiв в перколяцiйнiй точцi) зростала при збiльшеннi k. Для сумiшi k × k i m × m квадратiв (M-задача) величина pc сильно зростала при збiльшеннi k при фiксованому значеннi m та наближалась до 1 приk Ê 10m. Це пов’язано з тим, що перколяцiя бiльших активних квадратiв для M-задачi може ефективно пригнiчуватися за наявностi невеликої кiлькостi малих заблокованих квадратiв. Authors would like to acknowledge the partial financial support of project 43–02–14(U), Ukraine (N.L.) and of project RFBR 14–02–90402_Ukr, Russia (Yu.T.). Authors also thank Dr. N.S. Pivovarova for her help with the preparation of the manuscript. 2014 Article Jamming and percolation of parallel squares in single-cluster growth model / I.A. Kriuchevskyi, L.A. Bulavin, Yu.Yu. Tarasevich, N.I. Lebovka // Condensed Matter Physics. — 2014. — Т. 17, № 3. — С. 33006:1-11. — Бібліогр.: 42 назв.— англ. 1607-324X DOI:10.5488/CMP.17.33006 PACS: 02.70.Uu, 05.65.+b, 36.40.Mr, 61.46.Bc, 64.60.ah arXiv:1410.4292 https://nasplib.isofts.kiev.ua/handle/123456789/153448 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a square lattice were occupied by addition of the equal size k x k squares (E-problem) or a mixture of k x k and m x m (m ≤ k) squares (M-problem). The larger k x k squares were assumed to be active (conductive) and the smaller m x m squares were assumed to be blocked (non-conductive). For equal size k x k squares (E-problem) the value of pj = 0.638 ± 0.001 was obtained for the jamming concentration in the limit of k →∞. This value was noticeably larger than that previously reported for a random sequential adsorption model, pj = 0.564 ± 0.002. It was observed that the value of percolation threshold pc (i.e., the ratio of the area of active k x k squares and the total area of k x k squares in the percolation point) increased with an increase of k. For mixture of k x k and m x m squares (M-problem), the value of pc noticeably increased with an increase of k at a fixed value of m and approached 1 at k ≥ 10 m. This reflects that percolation of larger active squares in M-problem can be effectively suppressed in the presence of smaller blocked squares. |
| format |
Article |
| author |
Kriuchevskyi, I.A. Bulavin, L.A. Tarasevich, Yu.Yu. Lebovka, N.I. |
| spellingShingle |
Kriuchevskyi, I.A. Bulavin, L.A. Tarasevich, Yu.Yu. Lebovka, N.I. Jamming and percolation of parallel squares in single-cluster growth model Condensed Matter Physics |
| author_facet |
Kriuchevskyi, I.A. Bulavin, L.A. Tarasevich, Yu.Yu. Lebovka, N.I. |
| author_sort |
Kriuchevskyi, I.A. |
| title |
Jamming and percolation of parallel squares in single-cluster growth model |
| title_short |
Jamming and percolation of parallel squares in single-cluster growth model |
| title_full |
Jamming and percolation of parallel squares in single-cluster growth model |
| title_fullStr |
Jamming and percolation of parallel squares in single-cluster growth model |
| title_full_unstemmed |
Jamming and percolation of parallel squares in single-cluster growth model |
| title_sort |
jamming and percolation of parallel squares in single-cluster growth model |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2014 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/153448 |
| citation_txt |
Jamming and percolation of parallel squares in single-cluster growth model / I.A. Kriuchevskyi, L.A. Bulavin, Yu.Yu. Tarasevich, N.I. Lebovka // Condensed Matter Physics. — 2014. — Т. 17, № 3. — С. 33006:1-11. — Бібліогр.: 42 назв.— англ. |
| series |
Condensed Matter Physics |
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2025-11-25T22:33:38Z |
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