From f3dd4403222bedb3cdfbd33f6cdcef0c2d93bbce Mon Sep 17 00:00:00 2001
From: noah <noah@theschricks.com>
Date: Wed, 1 Feb 2023 16:23:56 -0600
Subject: [PATCH] Part 5: Bose-Einstein condensation in variable dimensionality

---
 Schrick-Noah_Project-2.R | 53 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 52 insertions(+), 1 deletion(-)

diff --git a/Schrick-Noah_Project-2.R b/Schrick-Noah_Project-2.R
index d0dd747..7c77b20 100644
--- a/Schrick-Noah_Project-2.R
+++ b/Schrick-Noah_Project-2.R
@@ -25,7 +25,7 @@ findZeroBisect <- function(func, xl, xr, tol, maxsteps=1e6){
 # Solve 1a
 fun.a <- function(x) {x^2-2}
 fun.a.string <- "x^2-2=0"
-sqrt2.estimate <- findZeroBisect(fun.a.string,1,2,1e-6)
+sqrt2.estimate <- findZeroBisect(fun.a,1,2,1e-6)
 # Plot 1a
 if (!require("ggplot2")) install.packages("ggplot2")
 library(ggplot2)
@@ -189,3 +189,54 @@ fb.estimate <- implicitFF(8000, 0.0001, 0)
 # 4c
 fc.estimate <- implicitFF(9000, 0.0001, 0)
 
+
+## Part 5: Bose-Einstein condensation in variable dimensionality
+# a:
+g <- 10000
+d <- 2
+l <- 0
+
+func.five <- function(u){
+  (-10000/(2*pi)) +
+  (u/2) *
+  sqrt((u^2)-((d+2*l)^2)/4) +
+  (((d+2*l)^2)/16) *
+  log((u-sqrt((u^2)-((d+2*l)^2)/4))/(u+sqrt((u^2)-((d+2*l)^2)/4)))
+}
+
+func.five.string <- "function"
+func.five.estimate <- findZeroBisect(func.five,50,75,1e-6)
+# Plot
+ggplot(data.frame(x=seq(1,80,.1)), aes(x)) + 
+  stat_function(fun=func.five, aes(col=func.five.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=func.five.estimate[1], 
+                 col = "bisection estimate"), show.legend=TRUE)+
+  ggtitle("zeroth-order dimensional perturbation theory approximation for the chemical potential of the Gross-Pitaevskii equation in d dimensions") +
+  xlab("x") + ylab("y") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
+
+# b:
+g <- 10000
+d <- 2
+l <- 1
+
+func.five <- function(u){
+  (-10000/(2*pi)) +
+    (u/2) *
+    sqrt((u^2)-((d+2*l)^2)/4) +
+    (((d+2*l)^2)/16) *
+    log((u-sqrt((u^2)-((d+2*l)^2)/4))/(u+sqrt((u^2)-((d+2*l)^2)/4)))
+}
+
+func.five.string <- "function"
+func.five.estimate <- findZeroBisect(func.five,50,75,1e-6)
+# Plot
+ggplot(data.frame(x=seq(5,80,.1)), aes(x)) + 
+  stat_function(fun=func.five, aes(col=func.five.string)) + 
+  geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+  geom_vline(aes(xintercept=func.five.estimate[1], 
+                 col = "bisection estimate"), show.legend=TRUE)+
+  ggtitle("zeroth-order dimensional perturbation theory approximation for the chemical potential of the Gross-Pitaevskii equation in d dimensions") +
+  xlab("x") + ylab("y") +
+  theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))