1 files changed, 272 insertions, 0 deletions
diff --git a/final-project/old/disp.jl b/final-project/old/disp.jl
new file mode 100644
index 0000000..18e0a1b
--- /dev/null
+++ b/final-project/old/disp.jl
@@ -0,0 +1,272 @@
+M = 10
+m = 1 # mass of particles
+
+function calculate_force(
+	left_pos,
+	middle_pos,
+	right_pos,
+	K,
+	alpha = 0.0,
+	beta = 1000.0,
+)
+	linear_force = K * (left_pos + right_pos - 2 * middle_pos)
+	quadratic_force = alpha * (left_pos - middle_pos)^2 + alpha * (right_pos - middle_pos)^2
+	cubic_force = beta * (left_pos - middle_pos)^3 + beta * (right_pos - middle_pos)^3
+
+	return linear_force + quadratic_force + cubic_force
+end
+
+function tendency!(du, u, p, t)
+	# unpack the params
+	N, K, m = p
+
+	# get the positions and momenta
+	qs = u[1:2:end]
+	ps = u[2:2:end]
+
+	# go over the points in the lattice and update the state
+	for i in 1:N-1
+		mass = m
+		if i == Int(N / 2)
+			mass = M
+		end
+
+		left_index = max(1, i - 1)
+		right_index = min(N, i + 1)
+
+		du[i*2-1] = ps[i] / mass
+		force = calculate_force(qs[left_index], qs[i], qs[right_index], K)
+		du[i*2] = force / mass
+	end
+
+	# make last point same as first
+	du[N*2-1] = du[1] = 0 # set to 0
+	du[N*2] = du[2] = 0
+
+
+	if t % 100000 == 0
+		println("TIME UPDATE: ", t)
+	end
+
+	# if ps[Int(N / 2)] / M >= 1
+	# 	println("(in sim!) Time: ", t, " Vel: ", ps[Int(N / 2)] / M)
+	# 	# println("Other Positions: ", qs)
+	# 	println("Other Velocities: ", ps, "\n")
+	# end
+end
+
+function get_initial_state(
+	N,
+	initial_displacement = 2,
+	initial_velocity = 0,
+)
+	state = zeros(2 * N)
+
+	middle_index = 2 * Int(N / 2) - 1 # middle mass
+	state[middle_index] = initial_displacement
+	state[middle_index+1] = initial_velocity * M
+	return state
+end
+
+using DifferentialEquations
+function run_simulation(
+	N,
+	K,
+	m,
+	final_time,
+	initial_displacement = 2,
+	initial_velocity = 0,
+)
+	println("Running simulation with N = $N, K = $K, m = $m, final_time = $final_time, initial_displacement = $initial_displacement, initial_velocity = $initial_velocity\n")
+	s_0 = get_initial_state(N, initial_displacement, initial_velocity)
+
+	calculate_energy(s_0)
+
+	# pack the params
+	p = N, K, m
+	t_span = (0.0, final_time)
+	prob = ODEProblem(tendency!, s_0, t_span, p)
+	sol = solve(prob, Tsit5(), reltol = 1e-5, abstol = 1e-5, maxiters = 1e10) # control simulation
+
+	calculate_energy(sol.u[end])
+
+	println("Done Running Sim!\n\n")
+	return sol
+end
+
+using Plots
+function animate_positions(
+	states,
+	time_steps,
+	time_min = 0,
+	time_max = 30,
+	red_threshold = 2,
+	shift = true,
+)
+	println("Animating positions")
+	anim = @animate for i in 1:length(time_steps)
+		t = time_steps[i]
+		if t < time_min
+			continue
+		end
+		if t > time_max
+			break
+		end
+		positions = states[i][1:2:end]
+		v_middle = states[i][Int(length(states[1]) / 2)] / M
+		p_middle = states[i][Int(length(states[1]) / 2)-1]
+		y_lims = shift ? (-3 + p_middle, 3 + p_middle) : (-3, 3)
+		# plot(positions, label = "t = $(round(t, digits = 3)), v_middle=$(round(v_middle, digits=3))", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", ylim = (-3, 3))
+		if v_middle >= red_threshold
+			plot(positions, label = "t = $(round(t, digits = 7)), v_middle=$(round(v_middle, digits=7))", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", ylim = y_lims,
+				color = :red, legend = :topright,
+			)
+		else
+			plot(positions, label = "t = $(round(t, digits = 7)), v_middle=$(round(v_middle, digits=7))", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", ylim = y_lims,
+				color = :blue, legend = :topright,
+			)
+		end
+	end
+	mp4(anim, "t/animate-positions.mp4", fps = 30)
+	println("Done animating positions")
+end
+
+function plot_starting_and_final_positions(
+	states,
+	time_steps,
+)
+	# plot the positions
+	middle_index = Int(length(states[1]) / 2) - 1
+	pos_init = [x - states[1][middle_index] for x in states[1][1:2:end]]
+	pos_final = [x - states[end][middle_index] for x in states[end][1:2:end]]
+	p1 = plot(pos_init, label = "Initial", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", title = "Positions Over Time")
+	plot!(p1, pos_final, label = "Final", marker = :circle)
+
+	# plot the vels
+	vels_init = [x / M for x in states[1][2:2:end]]
+	vels_final = [x / M for x in states[end][2:2:end]]
+	p2 = plot(states[1][2:2:end], label = "Initial", marker = :circle, xlabel = "Mass Number", ylabel = "Velocity", title = "Velocities Over Time")
+	plot!(p2, states[end][2:2:end], label = "Final t = $(time_steps[end])", marker = :circle)
+
+	# save the plots
+	savefig(p1, "t/initial-final-positions.png")
+	savefig(p2, "t/initial-final-velocities.png")
+end
+
+function analyize_vels(
+	states,
+	time_steps,
+	threshold = 1.975,
+)
+	println("Analyzing velocities:\n")
+	output = []
+	for i in 1:length(states)
+		v = states[i][Int(length(states[i]) / 2)] / M
+		if v >= threshold - 10e-6
+			push!(output, i)
+			println("Time: ", time_steps[i], " Vel: ", v)
+		end
+	end
+
+	data = []
+	for i in 1:length(states)
+		push!(data, states[i][Int(length(states[i]) / 2)])
+	end
+	p = plot(data, label = "Velocity Over Time", xlabel = "Time", ylabel = "Velocity")
+	savefig(p, "t/velocity-over-time.png")
+
+	println("\nDone!\n\n")
+	return output
+end
+
+function analyize_pos(
+	states,
+	time_steps,
+	threshold = 1.975,
+)
+	println("Analyzing positions:\n")
+	output = []
+	for i in 1:length(states)
+		if states[i][Int(length(states[i]) / 2)-1] >= threshold
+			push!(output, i)
+			println("Time: ", time_steps[i], " Position: ", states[i][Int(length(states[i]) / 2)])
+		end
+	end
+
+	# plot the first 10 seconds of Velocity
+	data = []
+	for i in 1:length(states)
+		if time_steps[i] > 10
+			break
+		end
+		push!(data, states[i][Int(length(states[i]) / 2)] - 1)
+	end
+	p = plot(data, label = "Position Over Time", xlabel = "Time", ylabel = "Position")
+	savefig(p, "t/pos-over-time.png")
+
+	println("\nDone!\n\n")
+	return output
+end
+
+function calculate_energy(state)
+	# calculate the kinetic energy
+	kinetic_energy = 0
+	vels = state[2:2:end]
+	for i in 1:N
+		mass = i == Int(N / 2) - 1 ? M : m
+		# calculate the kinetic energy
+		kinetic_energy += 0.5 * vels[i] * vels[i] / mass
+	end
+
+	# calcaute the potential energy
+	potential_energy = 0
+	pos = state[1:2:end]
+	for i in 1:N-1
+		left_index = max(1, i - 1)
+		right_index = min(N, i + 1)
+		potential_energy += 0.5 * K * (pos[left_index] - pos[i])^2
+		potential_energy += 0.5 * K * (pos[right_index] - pos[i])^2
+	end
+
+	# print the energy
+	println("Kinetic Energy: ", kinetic_energy)
+	println("Potential Energy: ", potential_energy)
+	println("Total Energy: ", kinetic_energy + potential_energy, "\n")
+end
+
+function plot_middle_mass_phase_space(states)
+	# get the index of the middle mass
+	middle_index = Int(length(states[1]) / 2) - 1
+	# build an array of the pos and vel over time
+	pos = []
+	vel = []
+	for i in 1:length(states)
+		push!(pos, states[i][middle_index])
+		push!(vel, states[i][middle_index+1])
+	end
+
+	# plot the phase space
+	p = plot(pos, vel, xlabel = "Position", ylabel = "Momentum", title = "Phase Space of Middle Mass in FPU", label = "Beta = 10, K = 1, N = 64, M = $M")
+
+	# save the plot
+	savefig(p, "t/phase-space.png")
+end
+
+
+# Run the simulation
+N = 64 # number of masses
+K = 1 # spring constant
+final_time = 1000 # seconds
+plot_data = []
+
+my_vel = 100
+
+sol = run_simulation(N, K, m, final_time, 0, my_vel)
+
+println("final time: ", sol.t[end])
+# s = sol.u[1:2:end]
+# analyize_vels(sol.u, sol.t, my_vel)
+# analyize_pos(sol.u, sol.t, 1.4)
+plot_starting_and_final_positions(sol.u, sol.t)
+# animate_positions(sol.u, sol.t, 0, 100, my_vel) # expect 80913.35854226245 for k=10?? rip
+plot_middle_mass_phase_space(sol.u)