Changes between Version 8 and Version 9 of u/johannjc/galactic_colonization


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Timestamp:
10/18/17 10:39:42 (7 years ago)
Author:
Jonathan
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  • u/johannjc/galactic_colonization

    v8 v9  
    3333== Simulation result ==
    3434
    35 Ran a simulation with periodic BC's, but particles enter from the right unsettled.  Also shifted the random velocities by the expected front velocity 3 v_rms.  (Click on the picture below for a movie)
     35|| Earth Params ||||
     36|| v_rms || 30 km/s ||
     37|| v_probe || 30 km/s ||
     38|| d_probe || 10 pc ||
     39|| launch_period || 1e4 yr ||
     40|| rho || 1e5/(50 pc)^3 ||
     41
     42Ran a simulation with periodic BC's and 10^4^ systems, but particles enter from the right unsettled and enter from the left settled.  Systems on the left half start settled.  Also shifted the random velocities by the expected front velocity ~3 v_rms due to the maxwellian distribution.  (Click on the picture below for a movie).  Settled systems are in red, probes in blue, and unsettled systems are not shown.
    3643
    3744[[Image(settled0099.png, width=800, link=attachment:settled.gif)]]
    3845
    3946
    40 Then fit the number of settled systems to a logistic curve
     47Then fit the number of settled systems at the 'steady state' to a logistic curve
    4148
    4249$\rho = \frac{\rho_{\max}}{1+\exp^{(x-x0)/L}}$
     
    4956where if we calculate $T_p (\mathcal{V}-v)$ we get $0.6 pc$
    5057
    51 The travel time to the nearest star is a factor of 3 longer than the launch period - and the travel time to the maximum probe range is another factor of 10 on top of that, so $.6 pc$ is definitely a lower bound.  There is also potentially a selection bias in that the fastest moving systems (those out in front) will likely target systems moving quickly in the other direction... 
     58The travel time to neighboring stars is a factor of 3 longer than the launch period - and the travel time to the maximum probe range is another factor of 10 on top of that, so $.6 pc$ is definitely a lower bound for the logistic growth rate.  There is also potentially a selection bias in that the fastest moving systems (those out in front) will see more systems traveling quickly in the other direction which can also explain the larger then expected value for $L$
    5259
     60
     61And for reference - here is the same setup, but with no velocity fluctuations
     62
     63[[Image(settled0099.2.png, width=800, link=attachment:settled.2.gif)]]
     64
     65