Biomod/2012/Titech/NanoJugglers/Simulation
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(→3. Translational Brownian displacement) 
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{{Titech/NanoJugglers/HEAD}}  {{Titech/NanoJugglers/HEAD}}  
=Simulation Models=  =Simulation Models=  
  +  ::[[Image:Simulation models.png800px]]  
==Physical principles for simulations==  ==Physical principles for simulations==  
:We confirm the movement of rocket on 2D plots in simulation.  :We confirm the movement of rocket on 2D plots in simulation.  
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==1. Driving forces from Bubble detachment==  ==1. Driving forces from Bubble detachment==  
  :Biomolecular  +  ===1.1. Calculation for Speed=== 
+  :'''Bubbles detachment helps Biomolecular Rocket go straightforward.'''  
+  :The Biomolecular Rocket is accelerated by a single bubble detachment every Δt<sub>d</sub> seconds .  
:Bubbles detachments occur when fixed time Δt<sub>d</sub> passed.  :Bubbles detachments occur when fixed time Δt<sub>d</sub> passed.  
  :We defined  +  :We defined radius changes of bubbles with time as following formula. 
+  ::[[Image:TNJFormula12.png250px]]  
:Δt<sub>d</sub> is defined as the time which is required bubbles to reach its detachment radius R<sub>d</sub>.  :Δt<sub>d</sub> is defined as the time which is required bubbles to reach its detachment radius R<sub>d</sub>.  
  :We defined  +  ::[[Image:TNJFormula13.png250px]] 
+  :We defined velocity v<sub>i</sub> produced by single detachment and Δt<sub>d</sub> as following formula.  
{  {  
    
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::[[Image:TNJFormula10.png250px]]  ::[[Image:TNJFormula10.png250px]]  
    
  ::[[Image:TNJ constant2.png  +  ::[[Image:TNJ constant2.png275px]] 
}  }  
+  ===1.2. 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 in the area where catalytic engines are still attacched.  
+  :Bubbles detachment supply the Biomolecular Rocket velocity of opposite direciton.  
+  width="30px"  
+  <br>  
+    
+  [[Image:Directional.jpg180px]]  
+  }  
==2. Fluid resistance==  ==2. Fluid resistance==  
  :Fluid resistance depends on the velocity of Biomolecular Rocket and viscosity of solution.  +  :'''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  :Resistance is defined as  
::[[Image:TNJFormula9.png200px]]  ::[[Image:TNJFormula9.png200px]]  
  :Therefore, acceleration of Biomolecular Rocket is  +  :Therefore, acceleration of the Biomolecular Rocket is 
+  {  
+    
::[[Image:TNJFormula4.png200px]]  ::[[Image:TNJFormula4.png200px]]  
  :  +   
+  ::[[Image:TNJConstant5.png300px]]  
+  }  
+  
==3. Translational Brownian displacement==  ==3. Translational Brownian displacement==  
:'''Translational Brownian movement prevents Biomolecular Rocket from going straight forward.'''  :'''Translational Brownian movement prevents Biomolecular Rocket from going straight forward.'''  
  :This is because body of  +  :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  :Translational displacement by Brownian movement is described as  
{  {  
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::[[Image:TNJFormula8.png200px]]  ::[[Image:TNJFormula8.png200px]]  
    
  ::[[Image:TNJconstant3.png  +  ::[[Image:TNJconstant3.png300px]] 
}  }  
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:Movement of Biomolecular Rocket is also much influenced by Rotatory Brownian Movement  :Movement of Biomolecular Rocket is also much influenced by Rotatory Brownian Movement  
:Rotatory changes by Brownian movement is described as  :Rotatory changes by Brownian movement is described as  
+  {  
+    
::[[Image:TNJFormula5.png200px]]  ::[[Image:TNJFormula5.png200px]]  
+    
+    
::[[Image:TNJFormula6.png200px]]  ::[[Image:TNJFormula6.png200px]]  
+    
+  ::[[Image:TNJconstant4.png400px]]  
+  }  
+  ::::::>back to [[Biomod/2012/Titech/NanoJugglers/Results#2.2._Numerical_estimation_of_the_speed_of_the_Biomolecular_RocketResults 2.2. Numerical estimation of the speed of the Biomolecular Rocket]]  
+  ::::::>back to [[Biomod/2012/Titech/NanoJugglers/Results#3.3._Directional_control_of_the_Biomolecular_Rocket_by_the_photoswitchable_DNA_systemResults 3.3 Directional control of Biomolecular Rocket by the photoswitchable DNA system]]  
  +  =Tools=  
  ==  +  *Scilab 
  +  =References=  
  +  *J. G. Gibbs and Y.P. Zhao (2009) ''Autonomously motile catalytic nanomotors by bubble propulsion.'' University of Georgia, Athens, Georgia 30602, USA, American Institute of Physics.  
  +  *V. A. KiriUov and V. P. Patskov (1979) ''SOME REGULARITIES OF BUBBLE GROWTH UNDER CHEMICAL REACTION.'' Institute of Catalysis, Novosibirsk, USSR, React. Kinet. Catal. Lett., Vol. 11, No. 1, 1519 (1979) 
Current revision
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
1.1. Calculation for Speed
 Bubbles detachment helps Biomolecular Rocket go straightforward.
 The Biomolecular Rocket is accelerated by a single bubble detachment every Δt_{d} seconds .
 Bubbles detachments occur when fixed time Δt_{d} passed.
 We defined radius changes of bubbles with time as following formula.
 Δt_{d} is defined as the time which is required bubbles to reach its detachment radius R_{d}.
 We defined velocity v_{i} produced by single detachment and Δt_{d} as following formula.
1.2. Directional Calculation
 Where bubbles generation occured is determined randomly on the hemisphere surface with catalytic engine.


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
Tools
 Scilab
References
 J. G. Gibbs and Y.P. Zhao (2009) Autonomously motile catalytic nanomotors by bubble propulsion. University of Georgia, Athens, Georgia 30602, USA, American Institute of Physics.
 V. A. KiriUov and V. P. Patskov (1979) SOME REGULARITIES OF BUBBLE GROWTH UNDER CHEMICAL REACTION. Institute of Catalysis, Novosibirsk, USSR, React. Kinet. Catal. Lett., Vol. 11, No. 1, 1519 (1979)