多相膜介观尺度模型的数学分析
Mathematical analysis of a mesoscale model for multiphase membranes
AI总结：
本文提出由两种两亲性脂质构成的多相膜介观连续介质模型，通过分析关键长度参数趋于零时的渐近约化，证明了相分离能量的 $Γ$-收敛，并在二维下构造了全能量向 Jülicher-Lipowsky 弯曲能量约化形式收敛的恢复序列。
摘要：
本文介绍了一种由两种不同类型两亲性脂质构成的膜的介观尺度连续介质模型。该模型扩展了 Peletier 和第二作者 [Arch. Ration. Mech. Anal. 193, 2009] 针对单相情形的工作。我们针对一个关键长度参数趋于任意小时向宏观尺度的渐近约化进行了数学分析。我们识别出能量中的两个主要贡献项：一项与整体结构的弯曲相关，另一项描述内部相分离的代价。我们证明了相分离能量向周界泛函的 $Γ$-收敛，并在二维情形下构造了全能量向带有相分离超曲面线张力贡献的 Jülicher-Lipowsky 弯曲能量二维约化形式收敛的恢复序列。
英文摘要：
In this paper we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author [Arch. Ration. Mech. Anal. 193, 2009] for the one-phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the $Γ$-convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the Jülicher-Lipowsky bending energy with a line tension contribution for phase separated hypersurfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
