Changes between Version 25 and Version 26 of u/afrank


Ignore:
Timestamp:
08/30/16 14:39:08 (8 years ago)
Author:
Adam Frank
Comment:

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  • u/afrank

    v25 v26  
    99== Begin with most general form.
    1010
    11 We begin with three coupled equations for the interaction between a eco-civilization population (N), a resource and which they draw energy from (R) and the state of the planetary environment (E).
     11We begin with three coupled equations for the interaction between a exo-civilization population (N), a resource and which they draw energy from (R) and the state of the planetary environment (E).
    1212
    1313$\frac{dN}{dt} =B_N - D_N + B_{RN}$
    … …  
    1818
    1919
    20 In the equations above generally B is used "birth" terms that increase the variable and D is used for "death" terms that decrease the variable though the meaning depends on the case.  Each there terms may have dependencies on the other variables (the "phase space" variables (N,R,E) and other parameters/constraints.
     20In the equations above generally B is used as "birth" terms that increase the variable and D is used for "death" terms that decrease the variable (though the meaning depends on the case).  Each terms may have dependencies on the other variables - the "phase space" variables (N,R,E) - and other parameters/constraints.
    2121
    2222In the above,
    … …  
    3232$D_{ER}$ is the modification of extraction/consumption rate of resource $R$ due to changes in planetary environmental state $E$.
    3333
    34 $H_E$ is measure of capacity of planetary environment to return to an pre-civilization equilibrium state ($E_o$).
     34$H_E$ is measure of capacity of planetary environment to return to an pre-civilization equilibrium state $E_o$.
    3535 
    36 $D_{NE}$ is the forcing of the planetary environment from pre-civilization equilibrium state ($E_o$) due to non-resource based population activity.
    37 
    38 $D_{RE}$ is the forcing of the planetary environment from pre-civilization equilibrium state ($E_o$) due to resource based population activity.
     36$D_{NE}$ is the forcing of the planetary environment from pre-civilization equilibrium state $E_o$ due to non-resource based population activity.
     37
     38$D_{RE}$ is the forcing of the planetary environment from pre-civilization equilibrium state $E_o$ due to resource based population activity.
    3939
    4040
    4141== Choosing forms for the terms.
    4242
    43 All alpha terms represent either growth rates or measures of the effect of variable $i$ on variable "j".
     43All alpha terms represent either growth rates or measures of the effect of variable $i$ on variable $j$.
    4444
    4545
    … …  
    5252$B_{RN} = \alpha_{RN} \beta_{NR} N R$
    5353
    54 where $\alpha_{RN}$ is the per captia additional birth rate gained from extraction/consumption of resource R and $\beta_{NR}$ is the per captia extraction/consumption rate of resource R
     54where $\alpha_{RN}$ is a measure of the additional birth rate gained from extraction/consumption of resource R and $\beta_{NR}$ is the per captia extraction/consumption rate of resource R
    5555
    5656$D_{NR} = \beta_{NR} N R$
    … …  
    5858$D_{ER} = \beta_{NR} N R (\frac{E}{E_c})$
    5959
    60 where $E_c$ is the critical environmental state beyond which $E>E_c$ resource extraction is no longer possible.
     60where $E_c$ is the critical environmental state beyond which $(E>E_c)$ resource extraction is no longer possible.
    6161
    6262$H_E = \alpha_E E (1- \frac{E}{E_o})$