Examples » Walker: Integrating the skew-normal SDE

Control file

title "Example problem"

walker

  term 10.0  # Max time
  dt 0.001   # Time step size
  npar 10000 # Number of particles
  ttyi 1000  # TTY output interval

  rngs
    mkl_r250 seed 1 end
  end

  skew-normal
    depvar m
    init zero
    coeff const
    ncomp 2
    T 1.0 3.5 end
    sigmasq 0.04 0.25 end
    lambda 100.0 -50.0 end
    rng mkl_r250
  end

  statistics
    interval 2
    <m1m1> <m2m2>
  end

  pdfs
    interval 10
    filetype txt
    policy overwrite
    centering elem
    format scientific
    precision 4
    p1( M1 : 1.0e-2 )
    p2( M2 : 1.0e-2 )
  end
end

Example run on 4 CPUs

./charmrun +p4 Main/walker -v -c ../../tmp/test.q -u 0.9

Results

The left figure shows the first two moments indicating convergence to a statistically stationary state. The right one shows the estimated PDFs with their analytical solution (see DiffEq/SkewNormal.h).

Gnuplot commands to reproduce the above plots:

plot "stat.txt" u 2:3 w l t "<M1>", "stat.txt" u 2:4 w l t "<M2>", "stat.txt" u 2:5 w l t "<m1m1>", "stat.txt" u 2:6 w l t "<m2m2>"
plot "pdf_p1.txt" w p, "pdf_p2.txt" w p, exp(-x*x/2/0.2/0.2)*(1+erf(100.0*x/sqrt(2)))/0.2/sqrt(2*pi) lt 1, exp(-x*x/2/0.5/0.5)*(1+erf(-50.0*x/sqrt(2)))/0.5/sqrt(2*pi) lt 2