Changes between Version 24 and Version 25 of u/ehansen/RT
- Timestamp:
- 09/14/11 12:56:30 (13 years ago)
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u/ehansen/RT
v24 v25 27 27 [[latex($y(t)=y_o e^{\gamma t}$)]]. 28 28 29 Taking the log of both sides yields: [[latex($\log{y(t)}=\log{y_o}+\ gamma t$)]].29 Taking the log of both sides yields: [[latex($\log{y(t)}=\log{y_o}+\lambda t$)]]. 30 30 31 Therefore, the slope of a [[latex($\log{y(t)}$)]] vs. [[latex($t$)]] plot would yield the growth rate [[latex($\ gamma$)]].31 Therefore, the slope of a [[latex($\log{y(t)}$)]] vs. [[latex($t$)]] plot would yield the growth rate [[latex($\lambda$)]]. 32 32 Said plot was created and used to determine which time period would be most appropriate for calculating the growth rate. 33 33 * [attachment:snapshot1.png Log(interface_position) Plot] 34 34 At early times (approximately t < 2.5), the simulation does not have enough resolution to measure such small changes in the interface position. At late times (approximately t > 4.0), the interface develops irregularities because the instability is entering the nonlinear regime. Therefore, this type of analysis only works between the two aforementioned times. 35 35 36 The plots were used to get a rough idea of when to calculate the growth rate. Bear2fix was then used to actually do the calculation directly from the data. The data does not actually need to be plotted to find the slope of a best fit line. Essentially, this slope (the growth rate) was calculated us edthe method of least squares.36 The plots were used to get a rough idea of when to calculate the growth rate. Bear2fix was then used to actually do the calculation directly from the data. The data does not actually need to be plotted to find the slope of a best fit line. Essentially, this slope (the growth rate) was calculated using the method of least squares. 37 37 == Results == 38 It can be shown that the analytic growth rate [[latex($\lambda_a=\sqrt{A g t}$)]]
