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Titlebook: Optimal Transportation Networks; Models and Theory Marc Bernot,Vicent Caselles,Jean-Michel Morel Book 2009 Springer-Verlag Berlin Heidelber

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發(fā)表于 2025-3-21 16:52:08 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Optimal Transportation Networks
副標(biāo)題Models and Theory
編輯Marc Bernot,Vicent Caselles,Jean-Michel Morel
視頻videohttp://file.papertrans.cn/703/702944/702944.mp4
概述Includes supplementary material:
叢書名稱Lecture Notes in Mathematics
圖書封面Titlebook: Optimal Transportation Networks; Models and Theory Marc Bernot,Vicent Caselles,Jean-Michel Morel Book 2009 Springer-Verlag Berlin Heidelber
描述.The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. .These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume..
出版日期Book 2009
關(guān)鍵詞Approximation; Irrigation; Monge-Kantorovich problem; Optimal transport; Traffic plans; Transportation ne
版次1
doihttps://doi.org/10.1007/978-3-540-69315-4
isbn_softcover978-3-540-69314-7
isbn_ebook978-3-540-69315-4Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2009
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沙發(fā)
發(fā)表于 2025-3-21 23:31:18 | 只看該作者
Book 2009In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigati
板凳
發(fā)表于 2025-3-22 04:27:15 | 只看該作者
0075-8434 n measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transp
地板
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Operations on Traffic Plans,tandard way to explicitly construct infinite irrigation trees, or patterns. Incidentally three elementary assumptions will be justified by their lack of incidence on the search of optimal traffic plans: X can be taken convex, the mass of χ can always be taken equal to one, and we can get rid of zero-length fibers.
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The Equivalence of Various Models, et al. . model [59]. Finally Section 9.3 treats the equivalence between traffic plans and Xia’s .. In all cases the equivalence is strong, as not only the minimal energies are the same but the minimizing objects, of very diverse nature, can be identified with each other. The presentation here follows [13]. Several tools come from [58] and [70].
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978-3-540-69314-7Springer-Verlag Berlin Heidelberg 2009
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