Changes between Version 20 and Version 21 of u/johannjc


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Timestamp:
06/16/12 18:12:46 (12 years ago)
Author:
Jonathan
Comment:

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  • u/johannjc

    v20 v21  
    5757 * Look at 'core' properties (though 2D and no SG)
    5858
    59 Heitsch et al 2006
    60  *
    61 
    62 == Random Ruminations ==
     59Heitsch et al 2006 "Birth of Molecular Clouds"
     60 * Extended 2005 work to 3D
     61 * no sg and hydro
     62 * sinusoidal interface
     63 * .5 particles/cc
     64 * periodic (open in 2D)
    6365
    6466
    65 So setting up the initial solution can be accomplished by the following:
     67Audit & Hennebelle 2005
     68 * 2D colliding flows
     69 
     70Heitsch et al 2006 "Magnetized Non-Linear thin shell instability -2D"
     71 * 2D MHD using PROTEUS
     72 * Fields weaken or suppress NTSI
    6673
    67 First start with the assumption that the retarted time is the current time
     74Heitsch et al 2006 "Cloud Dispersal in Turbulent Flows"
     75 * no sg- looked at turbulent dispersal of clouds
    6876
    69 [[latex($t_r=t$)]]
     77Heitsch, Stone, and Hartmann 2008 "Effects of Magnetic Field Strencth and Orientation on Molecular Cloud Formation"
     78
     79 * Athena 3D 256^3^ - no sg - mhd
     80 * Fields are important to resulting structure
     81 * Fields normal to flow favor filamentary structure in collision plane
     82 * Fields perpendicular to flow (ie y ) suppress ntsi along field axis (ky /= 0) and give an extended slab with filaments normal to field
    7083
    7184
    72 DO
    73 
    74   Calculate the displacement vector from the primary at the retarded time
    75 
    76   [[latex($\vec{d} = \vec{x}-\vec{X}_p(t_r)$)]]
    77 
    78   Calculate the wind normal so that
    79 
    80   [[latex($(v_w \hat{n} + \vec{V}_p(t_r)) \times \vec{d} = 0$)]]
    81  
    82   [[latex($\hat{n} \times \vec{d} = \frac{-1}{v_w}\vec{V}_p(t_r) \times \vec{d}$)]]
    83 
    84   It is possible to solve [[latex($\hat{a} \times \vec{b} = \vec{c}$)]] for the unit vector [[latex($\hat{a}$)]]
    85 
    86   [[latex($\hat{a}=\frac{\vec{b} \times \vec{c} + \sqrt{\vec{b} \cdot \vec{b} - \frac{(\vec{b} \times \vec{c}) \cdot (\vec{b} \times \vec{c})}{\vec{b} \cdot \vec{b}}} \vec{b}}{\vec{b} \cdot \vec{b}}$)]]
     85Heitsch, Hartmann, and Burkert "Fragmentation of Shocked Flows: Gravity, Turbulence, and Cooling"
     86 * Theory paper
     87 * Star formation happens soon after MC formation
     88 * Density enhancements are produced along with MC - problem with 'condensation models'
     89 * Nead non-linear density enhancements - faster than gravity
     90 * Discuss TI, GI, NTSI, KHI
     91 * Phase diagrams with lines outlining dominate instabilities
     92 * Dynamical and thermal instabilities dominate on small scales
     93 * Thermal fragmentatation dominates gravitational fragmentation during cloud formation
     94 * TI alone cannot produce jeans unstable clumps...  need additional global compression
    8795
    8896
    89   Once we have an estimate for [[latex($\hat{n}$)]] we can improve the estimate by modifying the trajectory to account for the gravity from the secondary as follows:
    9097
    91    Calculate the wind velocity from the primary
    92  
    93    [[latex($\vec{v}(t_r, x_p(t_r))=|v_w \hat{n}+\vec{V}_p(t_r)|$)]]
    9498
    95    Now solve for the trajectory from the primary that leaves at [[latex($\vec{X_p}(t_r)$)]] at velocity [[latex($\vec{v}(t_r, x_p(t_r))$)]] taking into account the force from the secondary. 
     99VazqueszSemadeni 2006
     100 * Velocity perturbations
    96101
    97    Determine the path's distance of closest approach to [[latex($\vec{x}$)]] and call that [[latex($\vec{x}'(t')$)]]
    98  
    99    Estimate the change in initial velocity needed [[latex($\vec{v'}(t_r,x_p(t_r) = \vec{v}(t_r,x_p(t_r))+\frac{x-x'(t')}{t'-t_r}$)]]
    100102
    101    And then solve for the unit vector that gives that direction
    102    
    103    [[latex($ \hat{n} \times \vec{v}' = \frac{-1}{v_w}\vec{V}_p(t_r) \times \vec{v}' $)]]
    104 
    105    
    106    Cycle until [[latex($x' \approx x$)]]
    107 
    108   Update the retarded time using the new distance and wind speed
    109 
    110   [[latex($t_r=t-(t'-t_r)$)]]
    111 
    112 END DO
    113 
    114 The only problem occurs when there are multiple solutions for the retarded time...
    115 
    116 This will occur once we reach distances of order [[latex($v_w/\Omega$)]]
    117 
    118 If we switch to a rotating frame that rotates counter to the orbit so the angular speed is [[latex($\Omega$)]], then
    119 
    120 [[latex($\vec{v}_r=\vec{v}-\Omega \times \vec{x}$)]]
    121 
    122 and
    123 
    124 [[latex($\alpha=\alpha_0+\Omega t$)]]
    125 
    126 so that
    127 
    128 [[latex($\Omega t_r+\alpha = \alpha_0 - \Omega \frac{d}{v_w}$)]]
     103Inoue and Inutsuka 2012
     104 * Colliding Flows in 3D
     105 * Richtmyer-Meshkov instability
     106 * No dynamical sg
     107 * 1024^3^