Consider a bead spring model for self avoiding polymer $($spherical particles connected with Hooken springs$).$ Consider the equilibrium length of the spring as l $=1$ and the radius of the bead as $\backslash$sigma $=0\mathrm{.}5.$ The potential of the spring is given by U$/$kBT $=1/2$k$($r$$l$)2,$ and between beads is given by V$/$kBT $=0\mathrm{.}5((\backslash$sigma $/$r$)12(\backslash$sigma $/$r$)6)$ where kBT $=1.$ After setting up the equation of motion numerically solve it and calculate the end to end distance $($the distance of the first bead and the last bead$)$ as a function of time for $5,10$ and $20$ bead systems. Also, plot the equilibrium end$-$to$-$end distance as a function of the number of beads. When you make the initial configuration keep at least one spring not equal to the equilibrium length.

Instructions

Numerically solve for the forces from the potential and solve the Newtons equation of motion using Euler method.

Solve this with a code in python.Consider a bead spring model for self avoiding polymer $($spherical particles connected with

Hooken springs$).$ Consider the equilibrium length of the spring as $l=1$ and the radius of the

bead as $=0\mathrm{.}5.$ The potential of the spring is given by $\frac{U}{k_B}T=\frac{1}{2}k(r-l{)}^2,$ and between

beads is given by $\frac{V}{k_B}T=0\mathrm{.}5((\frac{}{r}{)}^{1}2-(\frac{}{r}{)}^6)$ where $k_{B}T=1.$ After setting up the

equation of motion numerically solve it and calculate the end to end distance $($the distance

of the first bead and the last bead$)$ as a function of time for $5,10$ and $20$ bead systems. Also,

plot the equilibrium end$-$to$-$end distance as a function of the number of beads. When you

make the initial configuration keep at least one spring not equal to the equilibrium length.

Write a code in python to solve for the forces from the potential and solve the Newtons equation of motion

using Euler method.

Contents of the file to be uploaded: Program file $($source file$)$ with comments. A pdf with

your results, graph $($This shows how good you fit is$),$ discussion and commands for compiling

your program.

Contents of the file to be uploaded: Program file $($source file$)$ with comments. A pdf with your results, graph $($This shows how good you fit is$),$ discussion and commands for compiling your program.