A fast rotating King model
(Parameters are N=1000, W0=6, w0=0.9)
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Equipartition of kinetic energies
(Parameters are m2/m1=100, 10% heavy red stars, 90% light yellow stars)
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Hénon-Heiles movie ("Surfing through the energy!"): Short MPEG4,
Short WMV2 (for Windows Media Player),
Long MPEG4. These movies have been created with gnuplot from 400 / 1500 data files
for surfaces of section calculated with my toycode within a few days on a 3 GHz Pentium PC.
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A star cluster spiralling into the Galactic Center on a circular orbit,
N = 5000, M_cl = 10^6 M_sol, V0 = V_cir, King W0 = 9
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A star cluster spiralling into the Galactic Center on a rosette orbit,
N = 5000, M_cl = 10^6 M_sol, V0 = 0.5 V_cir, King W0 = 9
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A star cluster spiralling into the Galactic Center on an eccentric rosette orbit,
N = 5000, M_cl = 10^6 M_sol, V0 = 0.25 V_cir, King W0 = 9
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This is a collection of some of my plots. One the one hand, you can get an
impression what it means to do computational physics, on the other
hand, you should see how much fun it is! For most of the plots,
I used different integrators, like 4th and 8th order Runge-Kutta,
the Hermite scheme, or fancy ones, like a time-transformed 8th order
composition scheme where the highest accuracy was needed.
For the plotting itself, I used gnuplot, IDL and
Mathematica.
Poincaré section in the Hénon-Heiles potential
at E=0.02 (no chaos, plotted are all orbits at the instant of
crossing x=0 with v_x > 0)
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This time at E=0.125 (mixture of chaos and order, i.e. it is
a "system with divided phase space")
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The Lorenz Attractor
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The Rössler Attractor
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The Mandelbrot set (This was done on a really hot day when I could not
concentrate on my work... For this, you only need roughly 36 lines of code,
a complex multiplication and the absolute value of a complex number)
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Feigenbaum diagram for the logistic map. At the period doubling
bifurcations the periodic orbits get unstable, which leads to
chaos.
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The figure eight solution of the three-body problem, which is a
stable (!) periodic orbit whose proof of existence has been
established by A. Chenciner and R. Montgomery, Annals of Mathematics,
152, 881 (2000). All three particles have equal masses and move on
the same figure.
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A slightly disturbed figure eight solution: The particles move on
slightly different figures.
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"The three-body problem is the heart of physics!": A choreographic solution of the three-body problem, i.e. an
unstable periodic orbit discovered by Carles Simó, who discovered
over 300 of these periodic solutions. All three particles have equal masses
and move on the same figure. I always want to calculate the
dominant eigenvalue of the monodromy matrix...
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Numerical solution of Burrau's problem (sometimes
called the Pythagorean Three-Body Problem, since the particles
are initially located at the edges of a Pythagorean triangle).
It was first solved numerically by
Szebebehely & Peters, AJ 72, 876 (1967).
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Numerical solutions of the Lane-Emden equation for different
polytropic indices (n=0, n=1 and n=5 are analytical solutions!
Note the beautiful blue oscillating solution for n=1, which is
nothing else than sin(x)/x; the n=3 solution also oscillates,
but on much larger scales)
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The isothermal curl (one obtains such curls for polytropes
with n>5, but this is for the isothermal sphere...)
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The Hill surface in the tidal approximation (using Oort's constants
for the epicyclic motion, it's bonbon shaped)
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A Poincaré section in the tidal approximation at the
critical Jacobi integral with a Plummer potential
(all orbits crossing y=0 with v_y > 0)
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