Skip to content

Commit

Permalink
Update README.md
Browse files Browse the repository at this point in the history
details added
  • Loading branch information
108mk authored Oct 14, 2023
1 parent 7e22ed2 commit c9eeb73
Showing 1 changed file with 18 additions and 12 deletions.
30 changes: 18 additions & 12 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -2,22 +2,28 @@
## Requirements:

The only requirement is Python 3.8 or above
All used libraries are within Python standard module
All used libraries are within the Python standard module
You don't need to install any extra module

# Project details:
### $\spadesuit$ To study a $time\ dependent\ viscoelastic\ fluid$ that can be modelled by Maxwell-Voigt type description.
### To study a time-dependent viscoelastic fluid that can be modelled by Maxwell-Voigt type description.
![alt text](https://github.com/108mk/Random-Walk-Simulation-to-study-Anamolous-Diffusion/blob/f71bfa1af2486db9b9027e288b7d79fdd03e4011/demo%20images/maxwell%20voigt%20material.png?raw=true)
### $\spadesuit$ We simulated [Langevin equation](https://en.wikipedia.org/wiki/Langevin_equation#Harmonic_oscillator_in_a_fluid) (a Stochastic differential equation ) for this viscoelastic system-
# $m\cdot \ddot x = -\eta(t)\cdot \dot x -\kappa(t)\cdot x + \delta(t)$ ;
> where, $\delta(t)$ is Gaussian noise term
### $\spadesuit$ System under study:
> Take elasticity of the system: $\kappa (t),\ and$ viscosity of the system $\eta (t)$, defining the characteristic parameter of the system $\tau (t) \equiv \lambda (t) = \frac{\eta (t)}{\kappa (t)}$
### $\star$ Material-1: Exponential ageing $\rightarrow \lambda (t) = \exp (t/t_0)$
### $\star$ Material-2: Power law ageing $\rightarrow \lambda (t) = (t/t_0)^m $
### $\star$ The phenomena of 'ageing' is studied in microrheology via the Brownian motion of tracer bead particles. Hence, we appropriately modelled the materials and simulated the tracer bead trajectory for relevant insight.
### We simulated [Langevin equation](https://en.wikipedia.org/wiki/Langevin_equation#Harmonic_oscillator_in_a_fluid) (a Stochastic differential equation ) for this viscoelastic system-
👉 $m\cdot \ddot x = -\eta(t)\cdot \dot x -\kappa(t)\cdot x + \delta(t)$ ;

👉 where, $\delta(t)$ is Gaussian noise term
### ⭐ System under study:
Take elasticity of the system: $\kappa (t),\ and$ viscosity of the system $\eta (t)$, defining the characteristic parameter of the system $\tau (t) \equiv \lambda (t) = \frac{\eta (t)}{\kappa (t)}$
👉 Material-1: Exponential ageing $\rightarrow \lambda (t) = \exp (t/t_0)$

👉 Material-2: Power law ageing $\rightarrow \lambda (t) = (t/t_0)^m $

👉 The phenomena of 'ageing' is studied in microrheology via the Brownian motion of tracer bead particles. Hence, we appropriately modelled the materials and simulated the tracer bead trajectory for relevant insight.

![alt text](https://github.com/108mk/Random-Walk-Simulation-to-study-Anamolous-Diffusion/blob/f71bfa1af2486db9b9027e288b7d79fdd03e4011/demo%20images/trajectories.png?raw=true)
![alt text](https://github.com/108mk/Random-Walk-Simulation-to-study-Anamolous-Diffusion/blob/f71bfa1af2486db9b9027e288b7d79fdd03e4011/demo%20images/ett-1.png?raw=true)
![alt text](https://github.com/108mk/Random-Walk-Simulation-to-study-Anamolous-Diffusion/blob/f71bfa1af2486db9b9027e288b7d79fdd03e4011/demo%20images/ett-2.png?raw=true)
## $\left< R^2 \right>\ \rightarrow\ mean\ sqaured\ displacement\ and,\ \ t, \xi \rightarrow\ simulation\ time$
## 🌱 $My\ first\ humble\ contribution\ to\ Open-Source!!!$ 🌱

👉 $\left< R^2 \right>\ \rightarrow\ mean\ sqaured\ displacement\ and,\ \ t, \xi \rightarrow\ simulation\ time$

👉 🌱 $My\ first\ humble\ contribution\ to\ Open-Source!!!$ 🌱

0 comments on commit c9eeb73

Please sign in to comment.