# Biomod/2012/Titech/Nano-Jugglers/Simulation

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# Simulation Models

## Physical principles for simulations

We confirm the movement of rocket on 2D plots in simulation.
We assumed that movement of biomolecular rocket is affected by following four forces and dynamics in simulation.

## 1. Driving forces from Bubble detachment

Biomolecular rocket accelerates by a single bubble detachment every Δtd seconds .
Bubbles detachments occur when fixed time Δtd passed.
We defined radius of bubbles changes with time as following formula.
Δtd is defined as the time which is required bubbles to reach its detachment radius Rd.
We defined these vi and Δtd as following formula.

It helps Biomolecular Rocket go straightforward.

## 2. Fluid resistance

Fluid resistance decreases speed of Biomolecular Rocket.
Fluid resistance depends on the velocity of Biomolecular Rocket and viscosity of solution.
Resistance is defined as
Therefore, acceleration of Biomolecular Rocket is

## 3. Translational Brownian displacement

Translational Brownian movement prevents Biomolecular Rocket from going straight forward.
This is because body of rocket is so small and smaller particles can't be controlled under Brownian Movement.
Translational displacement by Brownian movement is described as

## 4. Rotatory Brownian changes

Rotatory Brownian movement decreases the directional controllability of Biomolecular Rocket.
Movement of Biomolecular Rocket is also much influenced by Rotatory Brownian Movement
Rotatory changes by Brownian movement is described as