Оptimization of the shape of booms in case of oil spill

Oil spills pose a serious threat to marine ecosystems, causing long-lasting environmental and economic consequences. To minimize damage, it is critically important to effectively limit the spread of pollution. One of the most common means in the fight against oil spills are booms — floating barriers that allow to localize the spill area and increase the efficiency of subsequent cleaning. However, the effectiveness of such barriers depends not only on the materials used, but also on their geometric configuration. In this regard, the task of minimizing the length of the boom necessary to cover a given spill area becomes urgent. In this paper, this problem is formulated as an isoperimetric optimization problem in the class of polygons. The problem of maximizing the area bounded by a polygon with a fixed perimeter and a fixed segment (for example, a section of shore) is investigated, provided that the boundary is a broken line rather than a smooth curve. It is proved that the optimal shape is achieved when the polygon is regular, that is, its sides and angles are equal. The results obtained can be used in the design of more efficient boom placement systems, contributing to lower material costs and improved environmental safety.

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