Commit 1ed63fd2 by Matthieu Schaller

### 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") ... ...
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