کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4499854 1624006 2016 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Pattern formations and optimal packing
ترجمه فارسی عنوان
تشکل های الگو و بسته بندی مطلوب
کلمات کلیدی
شکل گیری الگو؛ تقریبی ساختاری؛ بسته بندی بهینه؛ بسته بندی تصادفی
موضوعات مرتبط
علوم زیستی و بیوفناوری علوم کشاورزی و بیولوژیک علوم کشاورزی و بیولوژیک (عمومی)
چکیده انگلیسی


• A connection between pattern formations and optimal random packing is established.
• All the optimal structures are precisely described.
• Random optimal packings are described as optimal structures within classes of isomorphic graphs.

Patterns of different symmetries may arise after solution to reaction–diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction–diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction–diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematical Biosciences - Volume 274, April 2016, Pages 12–16
نویسندگان
,