Commit 1ed63fd2 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Added functional form of the gravity long-range force correction to the plotting script.

parent fab7734d
......@@ -104,6 +104,7 @@ theory/Multipoles/fmm_standalone.pdf
theory/Multipoles/potential.pdf
theory/Multipoles/potential_long.pdf
theory/Multipoles/potential_short.pdf
theory/Multipoles/force_short.pdf
m4/libtool.m4
m4/ltoptions.m4
......
......@@ -65,6 +65,7 @@ k_rs = k * r_s
# Newtonian solution
phi_newton = 1. / r
phit_newton = 1. / k**2
force_newton = 1. / r**2
def smoothstep(x): #S_2(x)
ret = 6*x**5 - 15*x**4 + 10*x**3
......@@ -73,15 +74,28 @@ def smoothstep(x): #S_2(x)
ret[x > 1] = 1.
return ret
def my_exp(x):
#return 1. + x + (x**2 / 2.) + (x**3 / 6.) + (x**4 / 24.) + (x**5 / 120.)# + (x**6 / 720.)
return exp(x)
def sigmoid(x):
return 1. / (1. + exp(-x))
return 1. / (1. + 1./my_exp(x))
#return x / sqrt(1. + x**2)
def d_sigmoid(x):
return my_exp(x) / ((my_exp(x) + 1)**2)
def swift_corr(x):
#return 2. * smoothstep(x/4. + 1./2.) - 1.
#return sigmoid(4. * x)
return 2 * sigmoid( 4 * x ) - 1
def d_swift_corr(x):
return 2 * d_sigmoid( 4 * x )
def csch(x): # hyperbolic cosecant
return 1. / sinh(x)
figure()
x = linspace(-4, 4, 100)
plot(x, special.erf(x), '-', color=colors[0])
......@@ -89,18 +103,24 @@ plot(x, swift_corr(x), '-', color=colors[1])
plot(x, x, '-', color=colors[2])
ylim(-1.1, 1.1)
xlim(-4.1, 4.1)
#plot(x, exp(x), '-', color=colors[0])
#plot(x, my_exp(x), '-', color=colors[1])
savefig("temp.pdf")
# Correction in real space
corr_short_gadget2 = special.erf(r / (2.*r_s))
corr_long_gadget2 = exp(-k**2*r_s**2)
corr_short_swift = swift_corr(r / (2.*r_s))
#corr_long_swift = (-15. / 1024.) * (12. * r_s * k * cos(4. * r_s * k) + (16. * r_s**2 * k**2 - 3.) * sin(4. * r_s * k)) / (k**5 * r_s**5)
corr_long_swift = k * r_s * math.pi / (2. * sinh(0.5 * math.pi * r_s * k))
#corr_long_swift = k * r_s * math.pi / (2. * sinh(0.5 * math.pi * r_s * k))
corr_long_swift = math.pi * k * r_s * csch(0.5 * math.pi * r_s * k) / 2.
eta_short_gadget2 = special.erfc(r / 2.*r_s) + (r / (r_s * math.sqrt(math.pi))) * exp(-r**2 / (4.*r_s**2))
eta_short_swift = (2. * r * d_swift_corr(r / (2.*r_s)) / r_s) - 2*sigmoid(2*r / (r_s)) + 2.
# Shortrange term
# Shortrange term2
phi_short_gadget2 = (1. / r ) * (1. - corr_short_gadget2)
phi_short_swift = (1. / r ) * (1. - corr_short_swift)
force_short_gadget2 = (1. / r**2) * eta_short_gadget2
force_short_swift = (1. / r**2) * eta_short_swift
# Long-range term
phi_long_gadget2 = (1. / r ) * corr_short_gadget2
......@@ -108,6 +128,9 @@ phi_long_swift = (1. / r ) * corr_short_swift
phit_long_gadget2 = corr_long_gadget2 / k**2
phit_long_swift = corr_long_swift / k**2
figure()
# Potential
......@@ -139,15 +162,11 @@ xlim(1.1*r_min/r_s, 0.9*r_max/r_s)
ylim(3e-3, 1.5)
ylabel("$\\chi_s(r)$", labelpad=-3)
# 1 - Correction
subplot(313, xscale="log", yscale="log")
#print corr_short_gadget2
#plot(r_rs, np.abs(1. - np.ones(np.size(r))), '--', lw=1.4, color=colors[0])
plot(r_rs, corr_short_gadget2, '-', lw=1.4, color=colors[2])
plot(r_rs, corr_short_swift, '-', lw=1.4, color=colors[3])
plot([1., 1.], [1e-5, 1e5], 'k-', alpha=0.5, lw=0.5)
plot(r_rs, np.ones(np.size(r)), 'k--', alpha=0.5, lw=0.5)
plot(r_rs, np.ones(np.size(r))*0.01, 'k--', alpha=0.5, lw=0.5)
......@@ -158,12 +177,58 @@ ylabel("$1 - \\chi_s(r)$", labelpad=-2)
yticks([1e-2, 1e-1, 1], ["$0.01$", "$0.1$", "$1$"])
xlabel("$r / r_s$", labelpad=-3)
#ylim(0, 0.95)
savefig("potential_short.pdf")
##################################################################################################
# Force
figure()
subplot(311, xscale="log", yscale="log")
plot(r_rs, force_newton, '--', lw=1.4, label="${\\rm Newtonian}$", color=colors[0])
plot(r_rs, force_short_gadget2, '-', lw=1.4, label="${\\rm Gadget}$", color=colors[2])
plot(r_rs, force_short_swift, '-', lw=1.4, label="${\\rm SWIFT}$", color=colors[3])
plot([1., 1.], [1e-5, 1e5], 'k-', alpha=0.5, lw=0.5)
xlim(1.1*r_min/ r_s, 0.9*r_max / r_s)
ylim(1.1/r_max**2, 0.9/r_min**2)
ylabel("$|\\mathbf{f}_s(r)|$", labelpad=-3)
yticks([1e-4, 1e-2, 1e0, 1e2], ["$10^{-4}$", "$10^{-2}$", "$10^{0}$", "$10^{2}$"])
legend(loc="upper right", frameon=True, handletextpad=0.1, handlelength=3.2, fontsize=8)
# Correction
subplot(312, xscale="log", yscale="log")
plot(r_rs, eta_short_gadget2, '-', lw=1.4, color=colors[2])
plot(r_rs, eta_short_swift, '-', lw=1.4, color=colors[3])
plot(r_rs, np.ones(np.size(r)), 'k--', alpha=0.5, lw=0.5)
plot(r_rs, np.ones(np.size(r))*0.01, 'k--', alpha=0.5, lw=0.5)
plot([1., 1.], [-1e5, 1e5], 'k-', alpha=0.5, lw=0.5)
yticks([1e-2, 1e-1, 1], ["$0.01$", "$0.1$", "$1$"])
xlim(1.1*r_min/r_s, 0.9*r_max/r_s)
ylim(3e-3, 1.5)
ylabel("$\\eta_s(r)$", labelpad=-3)
# 1 - Correction
subplot(313, xscale="log", yscale="log")
plot(r_rs, 1. - eta_short_gadget2, '-', lw=1.4, color=colors[2])
plot(r_rs, 1. - eta_short_swift, '-', lw=1.4, color=colors[3])
plot([1., 1.], [1e-5, 1e5], 'k-', alpha=0.5, lw=0.5)
plot(r_rs, np.ones(np.size(r)), 'k--', alpha=0.5, lw=0.5)
plot(r_rs, np.ones(np.size(r))*0.01, 'k--', alpha=0.5, lw=0.5)
xlim(1.1*r_min/r_s, 0.9*r_max/r_s)
ylim(3e-3, 1.5)
ylabel("$1 - \\eta_s(r)$", labelpad=-2)
yticks([1e-2, 1e-1, 1], ["$0.01$", "$0.1$", "$1$"])
xlabel("$r / r_s$", labelpad=-3)
savefig("force_short.pdf")
##################################################################################################
figure()
subplot(211, xscale="log", yscale="log")
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment