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

(Difference between revisions)
 Revision as of 02:28, 28 October 2012 (view source) (→3. Translational Brownian displacement)← Previous diff Revision as of 02:41, 28 October 2012 (view source) (→1. Driving forces from Bubble detachment)Next diff → Line 28: Line 28: ::[[Image:TNJ constant2.png|400px]] ::[[Image:TNJ constant2.png|400px]] |} |} + + ===Directional Calculation=== + :'''Where bubbles generation occured is determined randomly on the hemisphere surface with catalytic engine.''' + + :We defined angle θ as bubbles detachment direction. + :θ is determined by uniformed numbers. + :Bubbles detachment supply the Biomolecular Rocket velocity of opposite direciton. ==2. Fluid resistance== ==2. Fluid resistance==

# 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

### Calculation for Speed

Bubbles detachment helps Biomolecular Rocket go straightforward.
The Biomolecular Rocket is accelerated by a single bubble detachment every Δtd seconds .
Bubbles detachments occur when fixed time Δtd passed.
We defined radius changes of bubbles with time as following formula.
Δtd is defined as the time which is required bubbles to reach its detachment radius Rd.
We defined velocity vi produced by single detachment and Δtd as following formula.

### Directional Calculation

Where bubbles generation occured is determined randomly on the hemisphere surface with catalytic engine.
We defined angle θ as bubbles detachment direction.
θ is determined by uniformed numbers.
Bubbles detachment supply the Biomolecular Rocket velocity of opposite direciton.

## 2. Fluid resistance

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

## 3. Translational Brownian displacement

Translational Brownian movement prevents Biomolecular Rocket from going straight forward.
This is because body of the Biomolecular 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
>back to Results 2.2. Numerical estimation of the speed of the Biomolecular Rocket
>back to Results 3.3 Directional control of Biomolecular Rocket by the photo-switchable DNA system