\theta +28 \sin (2 \theta
   )+\sin (4 \theta )} {\nonumber}\\
   f^\theta_{{m}} &=& \frac{k T}{r}  2 \cot (\theta )  \label{middlef} 
   \end{aligned}$$

(100,35) (0,0)[[![Top left: Force along $\vec n_\theta$ exerted by 2 self-avoiding polymers on a point object, if the object is left of the two polymers (solid), between them (dashed) or right of them (dotted), in geometry ${\cal A}$. Top right: geometry ${\cal C}$. Two self-avoiding polymers fixed at $-L$, passing through a hole at $L$, and constrained to remain above and below the point $z$. Bottom: Equal probability lines (solid) and force flow lines (dashed) for geometry ${\cal F}$; plot-units are $L$.[]{data-label="f:6"}](./figures/2polyforce2 "fig:"){width="0.48\columnwidth"}]{}]{} (52,0)[[![Top left: Force along $\vec n_\theta$ exerted by 2 self-avoiding polymers on a point object, if the object is left of the two polymers (solid), between them (dashed) or right of them (dotted), in geometry ${\cal A}$. Top right: geometry ${\cal C}$. Two self-avoiding polymers fixed at $-L$, passing through a hole at $L$, and constrained to remain above and below the point $z$. Bottom: Equal probability lines (solid) and force flow lines (dashed) for geometry ${\cal F}$; plot-units are $L$.[]{data-label="f:6"}](./figures/geom2bis "fig:"){width="0.48\columnwidth"}]{}]{} (46,18.5)[$\theta$]{} (0,32)[$f$]{}

and $ f^\theta_{\mathrm{r}}(\theta)= - f^\theta_{\mathrm{l}}(\pi-\theta)$. This is plotted on Fig. \[f:6\]. Note that 