论文标题
高度两亲性混合物的一个最小化剂
Codimension One Minimizers of Highly Amphiphilic Mixtures
论文作者
论文摘要
我们提出了功能化的Cahn Hilliard（FCH）功能的修改形式，该功能模拟了溶剂中高度两亲的系统。如果在大量溶剂分子中分离的分子的能量过高，则分子是高度的。对于这样的系统，一旦两性分子组装成一种结构，分子很少交换回大块。高度的两亲性FCH功能具有有限的平滑度，并承认紧凑的关键点。在分子长度的极限接近0的情况下，我们考虑具有有界能量的序列，其支撑位于固定的固定编成一个界面的epsilon-邻居中。我们表明，FCH能量在下面均匀地界定，与epsilon> 0无关，并确定了序列切向变化的假设，这些序列可以保证存在二线型双层轮廓方程的近端存在，并显示有限的切向变异的序列具有lim inm in lim的平等。对于固定的编纂一个接口，我们构建有界的能量序列，该序列会收敛到双层曲线，而其他具有更大的切向变化的能量序列不会收敛到双层曲线，但其限制能量会违反LIM INF不平等，具体取决于能量参数。
We present a modified form of the Functionalized Cahn Hilliard (FCH) functional which models highly amphiphilic systems in solvent. A molecule is highly amphiphilic if the energy of a molecule isolated within the bulk solvent molecule is prohibitively high. For such systems once the amphiphilic molecules assemble into a structure it is very rare for a molecule to exchange back into the bulk. The highly amphiphilic FCH functional has a well with limited smoothness and admits compactly supported critical points. In the limit of molecular length epsilon approaches 0, we consider sequences with bounded energy whose support resides within an epsilon-neighborhood of a fixed codimension one interface. We show that the FCH energy is uniformly bounded below, independent of epsilon >0, and identify assumptions on tangential variation of sequences that guarantee the existence of subsequences that converge to a weak solution of a rescaled bilayer profile equation, and show that sequences with limited tangential variation enjoy a lim inf inequality. For fixed codimension one interfaces we construct bounded energy sequences which converge to the bilayer profile and others with larger tangential variation which do not converge to the bilayer profile but whose limiting energy can violate the lim inf inequality, depending upon the energy parameters.
