附着于探针的聚合物的粘附
Configurations of polymers attached to probes
摘要：
我们研究聚合物连接到球形（圆形）或抛物面（抛物面）探头在三（二）维。自避免和随机行走检查数值。附着于具有曲率半径$R$的探针尖端的尺寸为$R_0$的聚合物的行为对于比率$s=R_0/R$的大值和小值定性地不同。我们证明，缩放的顺应性（力常数的倒数）$S/R_0^2$，和缩放的聚合物终点$<x_\perp>/R$的平均位置可以表示为$s$的函数。缩放顺应性是各向异性的，并且当$R_0\sim R$时在平行于表面的方向上相当大。表征聚合物构型数量的指数$γ$从小$s$时的平面边界特征值$γ_1$跨越到大$s$时反映探针整体形状的值。对于一个球形探针的交叉是一个不受阻碍的聚合物，而对于一个抛物线探针，我们不能排除一个新的指数。
英文摘要：
We study polymers attached to spherical (circular) or paraboloidal (parabolic) probes in three (two) dimensions. Both self-avoiding and random walks are examined numerically. The behavior of a polymer of size $R_0$ attached to the tip of a probe with radius of curvature $R$, differs qualitatively for large and small values of the ratio $s=R_0/R$. We demonstrate that the scaled compliance (inverse force constant) $S/R_0^2$, and scaled mean position of the polymer end-point $<x_\perp>/R$ can be expressed as a function of $s$. Scaled compliance is anisotropic, and quite large in the direction parallel to the surface when $R_0\sim R$. The exponent $γ$, characterizing the number of polymer configurations, crosses over from a value of $γ_1$ - characteristic of a planar boundary - at small $s$ to one reflecting the overall shape of the probe at large $s$. For a spherical probe the crossover is to an unencumbered polymer, while for a parabolic probe we cannot rule out a new exponent.
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。
