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Approximate symmetry structure of the heat flow on perturbed flat revolution spaces | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 22 آبان 1405 اصل مقاله (1.61 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.34647.3215 | ||
| نویسندگان | ||
| Akram Mohammadpouri* 1؛ Zahra Ghaffarzad2 | ||
| 1Faculty of Mathematics, Statistics, and Computer Science, University of Tabriz, Tabriz, Iran. | ||
| 2Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran | ||
| چکیده | ||
| This paper studies heat conduction on slightly deformed flat surfaces of revolution: planes, cylinders, and cones. The reference geometry is defined by an arc-length-parametrized curve, and the perturbed surface arises from a small deformation of that curve. Expanding the metric tensor to first order yields the Laplace Beltrami operator at linear accuracy. Approximate Lie symmetries are computed for each canonical surface, and the analysis shows how infinitesimal generators change under the unit-speed constraint. While exact surfaces admit rotational Killing fields, real systems like deformed membranes and nanostructures involve small imperfections. The linear expansion reveals whether isometries are preserved or broken, offering a geometric framework for approximate symmetry reduction. The results apply to heat conduction in engineering components and to pattern formation in biological membranes. | ||
| کلیدواژه‌ها | ||
| Approximate Lie point symmetries؛ cone؛ cylinder؛ flat surfaces؛ heat equation؛ Laplace--Beltrami operator؛ perturbed surfaces of revolution | ||
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آمار تعداد مشاهده مقاله: 2 تعداد دریافت فایل اصل مقاله: 1 |
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