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Particle Paths Homework.Rmd
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Particle Paths Homework.Rmd
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---
title: "Displacement Field HW"
output: html_notebook
---
```{r}
# Set the working directory.
setwd("~/Desktop/geologyGeometryAdvancedStructure")
# Load the necessary R libraries.
source("library/all.R")
library("ggplot2") # To install ggplot, type install.packages("ggplot2") into the console.
library("gganimate") # to animate ggplots
library("gifski") # to render animated figures
library("magick") # for compositing GIFs
source("advancedStructureFunctions.R") # This is a companion file that contains some functions specifically written for this script.
```
```{r}
# The velocity gradient tensor L is a tensor that describes the velocity (speed + direction) of all points in space. In this homework, we will use work with the 2D case, in which L is a 2x2 matrix.
# L takes the form:
# | exDot gammaDot |
# L = | 0 -eyDot |
# Y
# |
# |
# |
# |
# ————————|—————————— X
# |
# |
# |
# |
# Below is an example of a velocity field
exDot = 0.05
gammaDot = 0
c = 0
eyDot = -exDot
#-exDot #this is true if volume is perserved, i.e. the material is incompressible
velGradTens = rbind(c(exDot, gammaDot),
c(c , eyDot))
# Plot the 2D velocity gradient in (x,y) space
plot2DVelocityFieldFromL(exDot, gammaDot, 0, eyDot , gridSpacing = 2.5)
t = 10
if (exDot == 0) {
posGradTens = rbind(c(exp(exDot*t), gammaDot * t ),
c(0 , exp(eyDot*t) ))
} else {
posGradTens = rbind(c(exp(exDot*t), gammaDot/exDot*sinh(exDot*t)),
c(0 , exp(eyDot*t) ))
}
plot2DCircleDisplacementFieldFromF(posGradTens[1,1], posGradTens[1,2], posGradTens[2,1], posGradTens[2,2])
#anim_save("GeneralShear.gif", animation=plot, height = 5, width = 10, units = "in", res = 150)
```
```{r}
plotParticles = plotParticlePaths(velGradTens, totalTime = t, numberOfIncrements = 100, gridSpacing = 2, superimposeStrain = FALSE, superimposeMaterialLine = FALSE, materialLineAngle = 45)
plotParticles
```
```{r}
plotParticlesAndStrain = plotParticlePaths(velGradTens, totalTime = t, numberOfIncrements = 100, gridSpacing = 2, superimposeStrain = TRUE, superimposeMaterialLine = FALSE, materialLineAngle = 45)
plotParticlesAndStrain[[1]]
plotParticlesAndStrain[[2]]
```
```{r}
plotParticlesStrainAndMaterial = plotParticlePaths(velGradTens, totalTime = t, numberOfIncrements = 100, gridSpacing = 2, superimposeStrain = TRUE, superimposeMaterialLine = TRUE, materialLineAngle = 150)
plotParticlesStrainAndMaterial[[1]]
plotParticlesStrainAndMaterial[[2]]
```
```{r}
# Make composit GIF
plot = plotParticlesStrainAndMaterial
aGIF = animate(plot[[1]], width = 920, height = 480)
bGIF <- animate(plot[[2]], width = 480, height = 480)
a_mgif <- image_read(aGIF)
b_mgif <- image_read(bGIF)
new_gif <- image_append(c(a_mgif[1], b_mgif[1]))
for(i in 2:100){
combined <- image_append(c(a_mgif[i], b_mgif[i]))
new_gif <- c(new_gif, combined)
}
#new_gif
anim_save("GeneralShear_materialLine48deg.gif", animation=new_gif)
#height = 5, width = 10, units = "in", res = 150)
```
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