Stoyanov阶跃群的解析性质：解，标度，平稳轮廓

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-05-30 DOI:10.1016/j.physd.2025.134755

Vassil Ivanov

{"title":"Stoyanov阶跃群的解析性质：解，标度，平稳轮廓","authors":"Vassil Ivanov","doi":"10.1016/j.physd.2025.134755","DOIUrl":null,"url":null,"abstract":"<div><div>Within the framework of the Stoyanov–Tonchev equation, which describes the surface height evolution during the vicinal sublimation process affected by the electromigration of the adatoms, we explore further the stationary profiles of step bunches towards obtaining a closed-form solution. For this particular case, we derive an explicit analytical result for the slope-height relation for the bunches, and many of the well-known scaling results for the height and width of the bunch. A novel analytical approximation for the bunch profile <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is derived, leading to a scaling relation for the minimal step-step distance in the bunch formed as a product of two parts - a special combination of the initial parameters, with the dimension of length, and a complementary one that contains only the number of steps in the bunch.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134755"},"PeriodicalIF":2.7000,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytical properties of Stoyanov step bunches: Solutions, scaling, stationary profiles\",\"authors\":\"Vassil Ivanov\",\"doi\":\"10.1016/j.physd.2025.134755\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Within the framework of the Stoyanov–Tonchev equation, which describes the surface height evolution during the vicinal sublimation process affected by the electromigration of the adatoms, we explore further the stationary profiles of step bunches towards obtaining a closed-form solution. For this particular case, we derive an explicit analytical result for the slope-height relation for the bunches, and many of the well-known scaling results for the height and width of the bunch. A novel analytical approximation for the bunch profile <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is derived, leading to a scaling relation for the minimal step-step distance in the bunch formed as a product of two parts - a special combination of the initial parameters, with the dimension of length, and a complementary one that contains only the number of steps in the bunch.</div></div>\",\"PeriodicalId\":20050,\"journal\":{\"name\":\"Physica D: Nonlinear Phenomena\",\"volume\":\"481 \",\"pages\":\"Article 134755\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2025-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica D: Nonlinear Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278925002325\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278925002325","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在Stoyanov-Tonchev方程的框架内（该方程描述了受吸附原子电迁移影响的邻近升华过程中的表面高度演变），我们进一步探索了台阶束的固定分布，以获得封闭形式的解。对于这种特殊情况，我们推导出束的斜率-高度关系的显式解析结果，以及束的高度和宽度的许多众所周知的标度结果。导出了束形曲线h(x)的一种新的解析近似，得到了束中最小阶跃距离的标度关系，该标度关系是由两部分组成的乘积-初始参数的特殊组合，具有长度的维度，而互补参数仅包含束中的阶数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Analytical properties of Stoyanov step bunches: Solutions, scaling, stationary profiles

Within the framework of the Stoyanov–Tonchev equation, which describes the surface height evolution during the vicinal sublimation process affected by the electromigration of the adatoms, we explore further the stationary profiles of step bunches towards obtaining a closed-form solution. For this particular case, we derive an explicit analytical result for the slope-height relation for the bunches, and many of the well-known scaling results for the height and width of the bunch. A novel analytical approximation for the bunch profile

h (x)

is derived, leading to a scaling relation for the minimal step-step distance in the bunch formed as a product of two parts - a special combination of the initial parameters, with the dimension of length, and a complementary one that contains only the number of steps in the bunch.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.